Find the attached files.· For each question submit an image or pdf of your solution. Each question...

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Find the attached files.· For each question submit an image or pdf of your solution. Each question is to be    uploaded separately and each will accept multiple files. · When the assignment is completed, press Submit at the end of the page · Do not round any number during calculating, always use the exact number till you get the final answer Excel Hint for finding critical values: · Two tailed t test  · Left tailed t test  or right tailed t test  1. A group of 8 students are asked to estimate the length of one minute without reference to any timers. The times they provided (in seconds) are given below: 	53 	67 	63 	55 	75 	58 	56 	62 Assuming the population is approximately normal and using a 0.05 significance level, test the claim that these provided times are indeed from a population with mean 60 seconds. a) State the null and alternative hypotheses. b) Calculate the test statistic (round it to 3 decimal places). c) Find the critical value (round it to 3 decimal places). d) Make a statistical conclusion. Do the results indicate that students are reasonably good at estimating the length of one minute? 2. A professor claims that the mean final mark for is greater than 65. A sample of 35 students shows the sample mean is 67 with standard deviation 15. Test the professor’s claim using a 0.05 significance level. a) State the null and alternative hypotheses. b) Calculate the test statistic (round it to 3 decimal places). c) Find the P -value (round it to 3 decimal places). d) Make a conclusion based on your answers in parts b) and c). e) Explain what would constitute a Type I error in this context. f) Explain what would constitute a Type II error in this context. 3. The data in the table below were obtained through a survey of randomly selected individuals in London 	Speeding Tickets Received Within the Last Year? 	 	Yes 	No 	Male 	30 	224 	Female 	27 	473 a) Find the probability of getting someone ticketed for speeding, given that the selected person is a man (round to 3 decimal places). b) Find the probability of getting someone ticketed for speeding, given that the selected person is a woman (round to 3 decimal places). c) Use a 0.01 level of significance to test the claim that men are more likely to receive a speeding ticket than women.  · To use normal approximation, check the sample size requirements · Calculate the test statistics (round to 3 decimal places). d) Find the critical value (round it to 3 decimal places). e) Make a conclusion based on your answer from part c) and d).  4. 10 Healthy adults’ initial temperature (Temp 1) have been measured while sitting still, then their temperatures are measured again after laying down (Temp 2).  	Subject 	1 	2 	3 	4 	5 	6 	7 	8 	9 	10 	11 	Temp 1 	37.51 	37.07 	37.20 	37.23 	37.38 	37.59 	37.28 	37.12 	37.55 	37.04 	37.78 	Temp 2 	37.17 	36.91 	36.70 	36.80 	36.96 	37.25 	37.11 	36.82 	37.36 	36.92 	37.22 a) To test the claim that the mean temperature difference is 0 while sitting still vs. laying down, state the null and alternative hypotheses. b) At  significance level, find the critical value (round to 3 decimal places).  c) Calculate the test statistics (round to 3 decimal places). d) Use Excel Data Analysis function, at 0.05 significance level, compare the two paired sample mean, submit a screenshot of the result output. (t Stat from the output should match your answer in part c). e) Based on your answer from c) or d), at  level, what is your conclusion? 5. Download the excel file “Births” for the data set. It uses the birth weights of boys and girls. Using Excel Data Analysis Tool, test the claim that girls have a lower mean weight than boys at 0.05 level of significance. Do not assume population variances are equal. Hint: Open Excel, Data – Data Analysis. See two pictures below. a) State the null and alternative hypotheses. b) Find the test statistic (round it to 3 decimal places) from Excel output c) Find the P -value (round it to 3 decimal places) from Excel output d) Find critical value from Excel output e) Make a statistical conclusion based on your answers in parts b) to d). 6. An agent for a real estate company wanted to predict the monthly rent for apartments based on the size of the apartment. The data ”Rent”  for a sample of 25 apartments is available for download from Brightspace.  Perform a t test for the slope to determine if a significant linear relationship between the size and the rent exists at the 0.05 level of significance.  a) Create a scatter plot using Excel. Using your official name as the chart title.  b) Use Excel CORREL to find the linear correlation coefficient r. c) Find test statistic from Excel Summary Output. d) Find p-value from Excel Summary Output e) Make a statistical conclusion based on your answers in parts c) and d). Note 1, for c) and d), please submit your Excel Summary Output. Note 2, hint for using Regression using Excel:   Girls 	Girl BIRTH WEIGHT	Boy BIRTH WEIGHT 	3500	3900 	800	2800 	2400	3700 	4200	4000 	3100	3400 	2000	1600 	2900	3500 	3300	3900 	2800	3000 	2500	3200 	4000	3300 	3100	300 	3000	4000 	3400	4500 	3500	3600 	1500	1700 	1600	3900 	900	3800 	3800	2200 	2100	1800 	2600	3500 	4300	3400 	3400	3000 	3300	4100 	3500	4100 	3000	2700 	3500	2900 	2900	3300 	3300	2800 	2500	3500 	2800	3700 	2800	3600 	3500	3300 	900	3700 	2700	4300 	3700	2600 	3500	3300 	3000	3200 	3400	3900 	4700	3600 	3300	3400 	2800	4100 	3300	3300 	3100	1500 	2400	2600 	4200	3300 	3200	3600 	2300	3800 	2900	2000 	3100	3000 	2700	3800 	4200	3600 	3500	3100 	3000	1500 	4000	600 	3600	1000 	3200	3200 	3500	3800 	2400	3900 	3100	3600 	2800	3400 	3800	3200 	2500	3600 	3100	3400 	3500	3600 	3700	2700 	3500	3500 	4300	3600 	2500	3400 	3100	3800 	3800	3400 	2800	3400 	3000	2700 	3600	2900 	2700	4100 	3300	4300 	2700	3500 	3700	3100 	3200	3400 	3800	3600 	2800	3800 	3600	2800 	2500	4900 	2600	3800 	3200	3600 	2600	3000 	3300	3200 	3300	3700 	2900	3400 	2900	4000 	3100	3900 	3000	2500 	1900	2800 	3100	3300 	3100	2900 	4300	3700 	3200	3300 	1800	3600 	3200	3100 	3000	3300 	3000	3500 	3200	2700 	3300	3700 	3100	4000 	3200	3700 	2600	2300 	3800	2900 	3200	3300 	3400	2600 	2300	2400 	3500	3300 	2600	3200 	3100	3800 	2800	2900 	3300	3400 	3000	3300 	3200	2700 	3400	3300 	2300	3000 	2900	2900 	2800	3900 	1900	4000 	3600	2900 	3600	3500 	4100	3700 	2200	3500 	3800	3800 	3000	3600 	3100	4000 	2600	3200 	3400	3600 	2000	4100 	3100	3500 	3600	3400 	1700	3300 	3300	3100 	3300	4000 	3700	3200 	3400	2700 	3100	3200 	3800	3100 	2600	3500 	3600	3700 	3600	3400 	3000	3600 	2800	3600 	2900	3000 	3600	3100 	2300	3500 	300	2900 	3300	3600 	3300	3300 	3400	3000 	2800	3300 	3400	4000 	1800	2700 	2400	3400 	2800	2900 	2900	2800 	2700	3400 	3300	2300 	2900	2900 	3600	2400 	3600	3600 	4600	3500 	3100	3500 	700	3800 	2600	2700 	2000	4000 	3300	2300 	2000	3600 	3700	4500 	3100	3300 	3600	2700 	1600	2600 	3000	3700 	2700	1600 	3200	3900 	4000	3100 	3400	4600 	3800	2500 	3700	3600 	3400	3400 	3300	3200 	2400	2800 	3600	2800 	2200	4300 	3100	3300 	2800	2800 	3700	2900 	3400	3300 	3100	3500 	3200	3200 	2400	3400 	800	3200 	2400 	3500 	1700 	3000 	3500 	2900 	3400 	4000 	3200 	4000   Sheet1 	Size_(sq._ft)	Rent_($) 	840	1975 	1440	2650 	1085	2175 	1242	2500 	728	1975 	1495	2700 	1126	2675 	736	1935 	690	1900 	966	2125 	1110	2400 	1285	2625 	1975	3275 	1369	2800 	1165	2400 	1235	2475 	1235	2075 	1249	2700 	1150	2200 	906	2175 	1361	2600 	1030	2675 	765	2175 	990	1800 	1200	2750

Radhika · Accepted Answer

· For each question submit an image or pdf of your solution. Each question is to be    uploaded separately and each will accept multiple files.
· When the assignment is completed, press Submit at the end of the page
· Do not round any number during calculating, always use the exact number till you get the final answer
Excel Hint for finding critical values:
· Two tailed t test
· Left tailed t test or right tailed t test
1. A group of 8 students are asked to estimate the length of one minute without reference to any timers. The times they provided (in seconds) are given below:
	53
	67
	63
	55
	75
	58
	56
	62
Assuming the population is approximately normal and using a 0.05 significance level, test the claim that these provided times are indeed from a population with mean 60 seconds.
a) State the null and alternative hypotheses.
b) Calculate the test statistic (round it to 3 decimal places).
c) Find the critical value (rounditto3decimalplaces).
d) Make a statistical conclusion.Do the results indicate that students are reasonably good at estimating the length of one minute?
Solution 1 : Pop ~ Normal (60, 1)
a) Null Hypothesis H0: Mean of time length is 60 seconds i.e., μ = 60 
Alternative Hypothesis H1: μ ≠ 60
b) Test Statistic :  Since the sample size is small, so we use t test for difference of means. 
Test Statistic : 
                        
c) Critical value : 23.752
d) Since the p value of the test statistic is less than 0.05 so we may reject H0 at 5% level of significance. Also the critical value t(0.05, 7) = 2.364 , which is less than the test statistic. Thus we cannot fix the sample mean at 60 seconds. It further indicates that the students results are reasonably not enough to estimate the length of one minute.   
2. Aprofessorclaimsthatthemeanfinal mark forisgreaterthan65.Asampleof35 students shows the sample mean is 67 with standard deviation 15. Test the professor’s claim using a 0.05 significance level.
a) Statethenullandalternativehypotheses.
b) Calculatetheteststatistic(rounditto3decimalplaces).
c) FindtheP-value(rounditto3decimalplaces).
d) Makeaconclusionbasedonyouranswersinpartsb)andc).
e) ExplainwhatwouldconstituteaTypeIerrorinthiscontext.
f) ExplainwhatwouldconstituteaTypeIIerrorinthiscontext.
Solution 2 : 
a) Null Hypothesis H0: μ > 65
Alternative Hypothesis H1:

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