I have attached 3 attached the homework and textbook. The homework is based on chapter 4. Also, professor wants us to show work. Thank you.
Hw 3 HW #3 1 1) Billboard has speculated that the average length of a song on one of today's popular CDs is 3.75 minutes with a standard deviation of 0.75 minutes. A randomly selected song of a particular new type of music is 5 minutes. Using the .05 level of significance, is this new type of music, represented by this one song, longer than popular songs in general? Use the five steps of hypothesis testing. ❶ Restate the question as a research hypothesis and a null hypothesis about the populations. ❷ Determine the characteristics of the comparison distribution. ❸ Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ Determine your sample’s score on the comparison distribution. ❺ Decide whether to reject the null hypothesis. a. Sketch the distributions involved. HW #3 2 2) A nutritionist wants to determine whether people who regularly drink one protein shake per day have lower cholesterol than people in general. In the general population, cholesterol is normally distributed with μ = 190 and σ = 30. Chandler Bing has followed the protein shake regimen for two months is randomly selected, and his cholesterol is 135. The nutritionist reported this result as "p < .01". is the nutritionist's claim accurate? use the five steps of hypothesis testing to verify the nutritionist's claim. ❶ restate the question as a research hypothesis and a null hypothesis about the populations. ❷ determine the characteristics of the comparison distribution. ❸ determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ determine your sample’s score on the comparison distribution. ❺ decide whether to reject the null hypothesis. hw #3 3 3) michael scott has been tasked with seeing how sales of paper at dunder mifflin is going. sales are currently at an average of 14 per day, with a standard deviation of 4 (the distribution of sales follows a normal curve). jan, his boss, wants to know whether the sales has to do with jim and pam’s new sales technique. she wants to know whether sales have worsened due to their new sales technique. they test this technique on andy, whose sales are at an average of 5. using the .05 significance level, what should the michael tell jan? solve this problem explicitly using all five steps of hypothesis testing and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution. ❶ restate the question as a research hypothesis and a null hypothesis about the populations. ❷ determine the characteristics of the comparison distribution. ❸ determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ determine your sample’s score on the comparison distribution. ❺ decide whether to reject the null hypothesis. hw #3 4 4) dr. merideth grey is interested in whether a new treatment for poison ivy would reduce symptoms more quickly than the current treatment. in general, the current treatment completely eliminates symptoms after an average of 6 days, with a standard deviation of 1.2 days. one randomly selected patient, derek, is given the new treatment and had no symptoms after 5 days. using the .05 level of significance, is the new treatment faster than the current one? use the five steps of hypothesis testing. ❶ restate the question as a research hypothesis and a null hypothesis about the populations. ❷ determine the characteristics of the comparison distribution. ❸ determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ determine your sample’s score on the comparison distribution. ❺ decide whether to reject the null hypothesis. a. sketch the distributions involved. hw #3 5 5) for each of the following, (a) say which two populations are being compared, (b) state the research hypothesis, (c) state the null hypothesis, and (d) say whether you should use a one-tailed or two-tailed test and why. a) do canadian children whose parents are college educated score higher than canadian children in general on reading ability? (a) say which two populations are being compared population 1: population 2: (b) state the research hypothesis (c) state the null hypothesis (d) say whether you should use a one-tailed or two-tailed test and why. b) do people who have seen a therapist have more or less self-awareness than the general population? (a) say which two populations are being compared population 1: population 2: (b) state the research hypothesis (c) state the null hypothesis (d) say whether you should use a one-tailed or two-tailed test and why. hw #3 6 6. pick two variables you would like to study. a) identify which is the independent variable and which is the dependent variable. b) what is your null hypothesis and what is your research hypothesis? c) what kind of testing would you do- one tailed or two tailed? why? d) what is your own prediction will be the outcome? this is an example- please come up with a different example on your own: i am going to study the relationship between age and # of zoos visited monthly. age = independent variable # of zoos visited = dependent variable null hypothesis: there is no different across different ages on how many zoos they have visited/month. research hypothesis: there is a difference across ages on how many zoos they have visited/month. i will do a two tailed test because i am unsure if there is a difference across age groups on how many zoos visited/month and want to consider any possibility. my own prediction: i think that younger kids and older people will have visited more zoos per month than those in their teens or young adults. 0205414338.pdf major formulas formula number the mean is the sum of the scores divided by the number of scores. m = gx n (2-1) the variance is the sum of the squared deviations of the scores from the mean, divided by the number of scores. sd 2 = g1x - m22 n (2-2) a z score is the raw score minus the mean, divided by the standard deviation. z = x - m sd (3-1) the variance of a distribution of means is the variance of the population of individuals divided by the number of individuals in each sample. �2m = �2 n (5-2) the effect size for the difference between two means is the difference between the population means divided by the population’s standard deviation. d = �1 - �2 � (6-1) the estimated population variance is the sum of the squared deviation scores divided by the number of scores minus 1. s 2 = g1x - m22 n - 1 = ss n - 1 (7-1) the variance of the distribution of means based on an estimated population variance is the estimated population variance divided by the number of scores in the sample. s2m = s2 n (7-5) the t score in a single sample t test, and a t test for dependent means (where you are using difference scores) is your sample’s mean minus the null hypothesis population mean, divided by the standard deviation of the distribution of means. t = m - � sm (7-7) the pooled estimate of the population variance is the degrees of freedom in the first sample divided by the total degrees of freedom (from both samples) multiplied by the population variance estimate based on the first sample, plus the degrees of freedom in the second sample divided by the total degrees of freedom multiplied by the population variance estimate based on the second sample. s2pooled = df1 dftotal 1s212 + df2dftotal1s 2 22 (8-1) the variance of the distribution of means for the first population (based on an estimated population variance) is the pooled estimate of the population variance divided by the number of participants in the sample from the first population. s2m1 = s2pooled n1 (8-2) the variance of the distribution of differences between means is the variance of the distribution of means for the first population (based on an estimated population variance) plus the variance of the distribution of means for the second population (based on an estimated population variance). s2difference = s2m1 + s 2 m2 (8-4) the t score in a t test for independent means is the difference between the two sample means divided by the standard deviation of the distribution of differences between means. t = m1 - m2 sdifference (8-7) the within-groups population variance estimate (or mean .01".="" is="" the="" nutritionist's="" claim="" accurate?="" use="" the="" five="" steps="" of="" hypothesis="" testing="" to="" verify="" the="" nutritionist's="" claim.="" ❶="" restate="" the="" question="" as="" a="" research="" hypothesis="" and="" a="" null="" hypothesis="" about="" the="" populations.="" ❷="" determine="" the="" characteristics="" of="" the="" comparison="" distribution.="" ❸="" determine="" the="" cutoff="" sample="" score="" on="" the="" comparison="" distribution="" at="" which="" the="" null="" hypothesis="" should="" be="" rejected.="" ❹="" determine="" your="" sample’s="" score="" on="" the="" comparison="" distribution.="" ❺="" decide="" whether="" to="" reject="" the="" null="" hypothesis.="" hw="" #3="" 3="" 3)="" michael="" scott="" has="" been="" tasked="" with="" seeing="" how="" sales="" of="" paper="" at="" dunder="" mifflin="" is="" going.="" sales="" are="" currently="" at="" an="" average="" of="" 14="" per="" day,="" with="" a="" standard="" deviation="" of="" 4="" (the="" distribution="" of="" sales="" follows="" a="" normal="" curve).="" jan,="" his="" boss,="" wants="" to="" know="" whether="" the="" sales="" has="" to="" do="" with="" jim="" and="" pam’s="" new="" sales="" technique.="" she="" wants="" to="" know="" whether="" sales="" have="" worsened="" due="" to="" their="" new="" sales="" technique.="" they="" test="" this="" technique="" on="" andy,="" whose="" sales="" are="" at="" an="" average="" of="" 5.="" using="" the="" .05="" significance="" level,="" what="" should="" the="" michael="" tell="" jan?="" solve="" this="" problem="" explicitly="" using="" all="" five="" steps="" of="" hypothesis="" testing="" and="" illustrate="" your="" answer="" with="" a="" sketch="" showing="" the="" comparison="" distribution,="" the="" cutoff="" (or="" cutoffs),="" and="" the="" score="" of="" the="" sample="" on="" this="" distribution.="" ❶="" restate="" the="" question="" as="" a="" research="" hypothesis="" and="" a="" null="" hypothesis="" about="" the="" populations.="" ❷="" determine="" the="" characteristics="" of="" the="" comparison="" distribution.="" ❸="" determine="" the="" cutoff="" sample="" score="" on="" the="" comparison="" distribution="" at="" which="" the="" null="" hypothesis="" should="" be="" rejected.="" ❹="" determine="" your="" sample’s="" score="" on="" the="" comparison="" distribution.="" ❺="" decide="" whether="" to="" reject="" the="" null="" hypothesis.="" hw="" #3="" 4="" 4)="" dr.="" merideth="" grey="" is="" interested="" in="" whether="" a="" new="" treatment="" for="" poison="" ivy="" would="" reduce="" symptoms="" more="" quickly="" than="" the="" current="" treatment.="" in="" general,="" the="" current="" treatment="" completely="" eliminates="" symptoms="" after="" an="" average="" of="" 6="" days,="" with="" a="" standard="" deviation="" of="" 1.2="" days.="" one="" randomly="" selected="" patient,="" derek,="" is="" given="" the="" new="" treatment="" and="" had="" no="" symptoms="" after="" 5="" days.="" using="" the="" .05="" level="" of="" significance,="" is="" the="" new="" treatment="" faster="" than="" the="" current="" one?="" use="" the="" five="" steps="" of="" hypothesis="" testing.="" ❶="" restate="" the="" question="" as="" a="" research="" hypothesis="" and="" a="" null="" hypothesis="" about="" the="" populations.="" ❷="" determine="" the="" characteristics="" of="" the="" comparison="" distribution.="" ❸="" determine="" the="" cutoff="" sample="" score="" on="" the="" comparison="" distribution="" at="" which="" the="" null="" hypothesis="" should="" be="" rejected.="" ❹="" determine="" your="" sample’s="" score="" on="" the="" comparison="" distribution.="" ❺="" decide="" whether="" to="" reject="" the="" null="" hypothesis.="" a.="" sketch="" the="" distributions="" involved.="" hw="" #3="" 5="" 5)="" for="" each="" of="" the="" following,="" (a)="" say="" which="" two="" populations="" are="" being="" compared,="" (b)="" state="" the="" research="" hypothesis,="" (c)="" state="" the="" null="" hypothesis,="" and="" (d)="" say="" whether="" you="" should="" use="" a="" one-tailed="" or="" two-tailed="" test="" and="" why.="" a)="" do="" canadian="" children="" whose="" parents="" are="" college="" educated="" score="" higher="" than="" canadian="" children="" in="" general="" on="" reading="" ability?="" (a)="" say="" which="" two="" populations="" are="" being="" compared="" population="" 1:="" population="" 2:="" (b)="" state="" the="" research="" hypothesis="" (c)="" state="" the="" null="" hypothesis="" (d)="" say="" whether="" you="" should="" use="" a="" one-tailed="" or="" two-tailed="" test="" and="" why.="" b)="" do="" people="" who="" have="" seen="" a="" therapist="" have="" more="" or="" less="" self-awareness="" than="" the="" general="" population?="" (a)="" say="" which="" two="" populations="" are="" being="" compared="" population="" 1:="" population="" 2:="" (b)="" state="" the="" research="" hypothesis="" (c)="" state="" the="" null="" hypothesis="" (d)="" say="" whether="" you="" should="" use="" a="" one-tailed="" or="" two-tailed="" test="" and="" why.="" hw="" #3="" 6="" 6.="" pick="" two="" variables="" you="" would="" like="" to="" study.="" a)="" identify="" which="" is="" the="" independent="" variable="" and="" which="" is="" the="" dependent="" variable.="" b)="" what="" is="" your="" null="" hypothesis="" and="" what="" is="" your="" research="" hypothesis?="" c)="" what="" kind="" of="" testing="" would="" you="" do-="" one="" tailed="" or="" two="" tailed?="" why?="" d)="" what="" is="" your="" own="" prediction="" will="" be="" the="" outcome?="" this="" is="" an="" example-="" please="" come="" up="" with="" a="" different="" example="" on="" your="" own:="" i="" am="" going="" to="" study="" the="" relationship="" between="" age="" and="" #="" of="" zoos="" visited="" monthly.="" age="independent" variable="" #="" of="" zoos="" visited="dependent" variable="" null="" hypothesis:="" there="" is="" no="" different="" across="" different="" ages="" on="" how="" many="" zoos="" they="" have="" visited/month.="" research="" hypothesis:="" there="" is="" a="" difference="" across="" ages="" on="" how="" many="" zoos="" they="" have="" visited/month.="" i="" will="" do="" a="" two="" tailed="" test="" because="" i="" am="" unsure="" if="" there="" is="" a="" difference="" across="" age="" groups="" on="" how="" many="" zoos="" visited/month="" and="" want="" to="" consider="" any="" possibility.="" my="" own="" prediction:="" i="" think="" that="" younger="" kids="" and="" older="" people="" will="" have="" visited="" more="" zoos="" per="" month="" than="" those="" in="" their="" teens="" or="" young="" adults.="" 0205414338.pdf="" major="" formulas="" formula="" number="" the="" mean="" is="" the="" sum="" of="" the="" scores="" divided="" by="" the="" number="" of="" scores.="" m="gX" n="" (2-1)="" the="" variance="" is="" the="" sum="" of="" the="" squared="" deviations="" of="" the="" scores="" from="" the="" mean,="" divided="" by="" the="" number="" of="" scores.="" sd="" 2="g1X" -="" m22="" n="" (2-2)="" a="" z="" score="" is="" the="" raw="" score="" minus="" the="" mean,="" divided="" by="" the="" standard="" deviation.="" z="X" -="" m="" sd="" (3-1)="" the="" variance="" of="" a="" distribution="" of="" means="" is="" the="" variance="" of="" the="" population="" of="" individuals="" divided="" by="" the="" number="" of="" individuals="" in="" each="" sample.="" �2m="�2" n="" (5-2)="" the="" effect="" size="" for="" the="" difference="" between="" two="" means="" is="" the="" difference="" between="" the="" population="" means="" divided="" by="" the="" population’s="" standard="" deviation.="" d="�1" -="" �2="" �="" (6-1)="" the="" estimated="" population="" variance="" is="" the="" sum="" of="" the="" squared="" deviation="" scores="" divided="" by="" the="" number="" of="" scores="" minus="" 1.="" s="" 2="g1X" -="" m22="" n="" -="" 1="SS" n="" -="" 1="" (7-1)="" the="" variance="" of="" the="" distribution="" of="" means="" based="" on="" an="" estimated="" population="" variance="" is="" the="" estimated="" population="" variance="" divided="" by="" the="" number="" of="" scores="" in="" the="" sample.="" s2m="S2" n="" (7-5)="" the="" t="" score="" in="" a="" single="" sample="" t="" test,="" and="" a="" t="" test="" for="" dependent="" means="" (where="" you="" are="" using="" difference="" scores)="" is="" your="" sample’s="" mean="" minus="" the="" null="" hypothesis="" population="" mean,="" divided="" by="" the="" standard="" deviation="" of="" the="" distribution="" of="" means.="" t="M" -="" �="" sm="" (7-7)="" the="" pooled="" estimate="" of="" the="" population="" variance="" is="" the="" degrees="" of="" freedom="" in="" the="" first="" sample="" divided="" by="" the="" total="" degrees="" of="" freedom="" (from="" both="" samples)="" multiplied="" by="" the="" population="" variance="" estimate="" based="" on="" the="" first="" sample,="" plus="" the="" degrees="" of="" freedom="" in="" the="" second="" sample="" divided="" by="" the="" total="" degrees="" of="" freedom="" multiplied="" by="" the="" population="" variance="" estimate="" based="" on="" the="" second="" sample.="" s2pooled="df1" dftotal="" 1s212="" +="" df2dftotal1s="" 2="" 22="" (8-1)="" the="" variance="" of="" the="" distribution="" of="" means="" for="" the="" first="" population="" (based="" on="" an="" estimated="" population="" variance)="" is="" the="" pooled="" estimate="" of="" the="" population="" variance="" divided="" by="" the="" number="" of="" participants="" in="" the="" sample="" from="" the="" first="" population.="" s2m1="S2Pooled" n1="" (8-2)="" the="" variance="" of="" the="" distribution="" of="" differences="" between="" means="" is="" the="" variance="" of="" the="" distribution="" of="" means="" for="" the="" first="" population="" (based="" on="" an="" estimated="" population="" variance)="" plus="" the="" variance="" of="" the="" distribution="" of="" means="" for="" the="" second="" population="" (based="" on="" an="" estimated="" population="" variance).="" s2difference="S2M1" +="" s="" 2="" m2="" (8-4)="" the="" t="" score="" in="" a="" t="" test="" for="" independent="" means="" is="" the="" difference="" between="" the="" two="" sample="" means="" divided="" by="" the="" standard="" deviation="" of="" the="" distribution="" of="" differences="" between="" means.="" t="M1" -="" m2="" sdifference="" (8-7)="" the="" within-groups="" population="" variance="" estimate="" (or=""> .01". is the nutritionist's claim accurate? use the five steps of hypothesis testing to verify the nutritionist's claim. ❶ restate the question as a research hypothesis and a null hypothesis about the populations. ❷ determine the characteristics of the comparison distribution. ❸ determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ determine your sample’s score on the comparison distribution. ❺ decide whether to reject the null hypothesis. hw #3 3 3) michael scott has been tasked with seeing how sales of paper at dunder mifflin is going. sales are currently at an average of 14 per day, with a standard deviation of 4 (the distribution of sales follows a normal curve). jan, his boss, wants to know whether the sales has to do with jim and pam’s new sales technique. she wants to know whether sales have worsened due to their new sales technique. they test this technique on andy, whose sales are at an average of 5. using the .05 significance level, what should the michael tell jan? solve this problem explicitly using all five steps of hypothesis testing and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution. ❶ restate the question as a research hypothesis and a null hypothesis about the populations. ❷ determine the characteristics of the comparison distribution. ❸ determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ determine your sample’s score on the comparison distribution. ❺ decide whether to reject the null hypothesis. hw #3 4 4) dr. merideth grey is interested in whether a new treatment for poison ivy would reduce symptoms more quickly than the current treatment. in general, the current treatment completely eliminates symptoms after an average of 6 days, with a standard deviation of 1.2 days. one randomly selected patient, derek, is given the new treatment and had no symptoms after 5 days. using the .05 level of significance, is the new treatment faster than the current one? use the five steps of hypothesis testing. ❶ restate the question as a research hypothesis and a null hypothesis about the populations. ❷ determine the characteristics of the comparison distribution. ❸ determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ❹ determine your sample’s score on the comparison distribution. ❺ decide whether to reject the null hypothesis. a. sketch the distributions involved. hw #3 5 5) for each of the following, (a) say which two populations are being compared, (b) state the research hypothesis, (c) state the null hypothesis, and (d) say whether you should use a one-tailed or two-tailed test and why. a) do canadian children whose parents are college educated score higher than canadian children in general on reading ability? (a) say which two populations are being compared population 1: population 2: (b) state the research hypothesis (c) state the null hypothesis (d) say whether you should use a one-tailed or two-tailed test and why. b) do people who have seen a therapist have more or less self-awareness than the general population? (a) say which two populations are being compared population 1: population 2: (b) state the research hypothesis (c) state the null hypothesis (d) say whether you should use a one-tailed or two-tailed test and why. hw #3 6 6. pick two variables you would like to study. a) identify which is the independent variable and which is the dependent variable. b) what is your null hypothesis and what is your research hypothesis? c) what kind of testing would you do- one tailed or two tailed? why? d) what is your own prediction will be the outcome? this is an example- please come up with a different example on your own: i am going to study the relationship between age and # of zoos visited monthly. age = independent variable # of zoos visited = dependent variable null hypothesis: there is no different across different ages on how many zoos they have visited/month. research hypothesis: there is a difference across ages on how many zoos they have visited/month. i will do a two tailed test because i am unsure if there is a difference across age groups on how many zoos visited/month and want to consider any possibility. my own prediction: i think that younger kids and older people will have visited more zoos per month than those in their teens or young adults. 0205414338.pdf major formulas formula number the mean is the sum of the scores divided by the number of scores. m = gx n (2-1) the variance is the sum of the squared deviations of the scores from the mean, divided by the number of scores. sd 2 = g1x - m22 n (2-2) a z score is the raw score minus the mean, divided by the standard deviation. z = x - m sd (3-1) the variance of a distribution of means is the variance of the population of individuals divided by the number of individuals in each sample. �2m = �2 n (5-2) the effect size for the difference between two means is the difference between the population means divided by the population’s standard deviation. d = �1 - �2 � (6-1) the estimated population variance is the sum of the squared deviation scores divided by the number of scores minus 1. s 2 = g1x - m22 n - 1 = ss n - 1 (7-1) the variance of the distribution of means based on an estimated population variance is the estimated population variance divided by the number of scores in the sample. s2m = s2 n (7-5) the t score in a single sample t test, and a t test for dependent means (where you are using difference scores) is your sample’s mean minus the null hypothesis population mean, divided by the standard deviation of the distribution of means. t = m - � sm (7-7) the pooled estimate of the population variance is the degrees of freedom in the first sample divided by the total degrees of freedom (from both samples) multiplied by the population variance estimate based on the first sample, plus the degrees of freedom in the second sample divided by the total degrees of freedom multiplied by the population variance estimate based on the second sample. s2pooled = df1 dftotal 1s212 + df2dftotal1s 2 22 (8-1) the variance of the distribution of means for the first population (based on an estimated population variance) is the pooled estimate of the population variance divided by the number of participants in the sample from the first population. s2m1 = s2pooled n1 (8-2) the variance of the distribution of differences between means is the variance of the distribution of means for the first population (based on an estimated population variance) plus the variance of the distribution of means for the second population (based on an estimated population variance). s2difference = s2m1 + s 2 m2 (8-4) the t score in a t test for independent means is the difference between the two sample means divided by the standard deviation of the distribution of differences between means. t = m1 - m2 sdifference (8-7) the within-groups population variance estimate (or mean>