I need the following questions answered and to show work.
MAT102Test4print For #1-10 (a) State the null and alternative hypotheses (b) Calculate the expected results for the hypothesis test assuming the null hypothesis is true and determine the hypothesis test model , i.e., “cut-off” critical values etc. (c) Formulate the decision rule, i.e., include “one-tail ”left, or “one-tail” right, or “two-tail” determination etc. (d) Determine the experimental outcome. (e) Determine the conclusion, and answer the question(s) posed in the problem, if any. (1) It is claimed that a large corporation discriminates against its women employees in its promotion practices. Over many years, the mean time before first promotion for its male employees has been 3 years. A random sample of 20 females, who had worked there many years, showed a mean time of 3.8 years before first promotion, with s=1.2 years. Using a level of significance of 5%, see if the data support the claim. (2) The average IQ of a group of researchers is quoted to be 260. Thinking that this figure is too large, a consulting firm tested a random sample of 8 researchers and found that the average IQ was 250 with s=8. Test at a level of significance of 1%. (3) A claim is made that the mean height of police officers is 5 feet 11 inches. To test whether this claim is true or not, a random sample of 25 police officers was gathered. This sample had a mean height of 5 feet 10 inches with s=3 inches. Test at the 5% significance level. (4) To test whether or not there is a difference between the mean grade point averages of male math majors and female math majors at a certain university, 2 random samples were gathered. For the 35 males we find that the sample mean is 3.1 with s=0.2. For the 20 females, the sample mean is 3.2 with s=0.15. Test at a 1% level of significance. (5) Are “krispy toasters” quicker than “No-burn toasters” at the 1% significance level, if the times it took to toast a slice of bread were as follows: No-Burn: 60,55,70,65,80 seconds Krispy: 70,65,65,60,60 seconds ? (6) The mean score on a standardized psychology test is supposed to be 50. Believing that a group of psychologists will score higher, we test a random sample of 11 psychologists. Their mean score is 45 with s=3. Test at a 1% level of significance. (7) On field trips, science classes collect toads in a swamp. In June, 50 toads were caught with a mean weight of 1.1 ounces and with s=0.05 ounce. In August 25, toads were caught with a mean weight of 2.1 ounces and s=0.07 ounce. Does this indicate at the 1% significance level that August toads are heavier than June toads? (8) Is there a statistically significant difference between the bowling averages of male nurses and those of businessmen, if last year’s league play produced the following data: 10 male nurses averaged 180 with s=10, and 15 businessmen averaged 170 with s=10? Use 5% level of significance. (9) To see whether there is a statistically significant difference between the age of owners of convertibles and the age of owners of sedans, an advertising agency found that 15 convertible owners had an average age of 29.2 years with s=5, and 35 sedan owners had an average age of 24.8 years with s=8. Test at a 5% level of significance. (10) An astronomer is testing the claim that the mean brightness of a certain star is now more than 30 units. The astronomer is able to get 6 readings on the star during an experiment as shown in the table. Using a 1% level of significance, does this indicate a new mean brightness of more than 30? Reading Brightness 1 30 2 30 3 29 4 31 5 32 6 33 MAT102Test4print For #1-10 (a) State the null and alternative hypotheses (b) Calculate the expected results for the hypothesis test assuming the null hypothesis is true and determine the hypothesis test model , i.e., “cut-off” critical values etc. (c) Formulate the decision rule, i.e., include “one-tail ”left, or “one-tail” right, or “two-tail” determination etc. (d) Determine the experimental outcome. (e) Determine the conclusion, and answer the question(s) posed in the problem, if any. (1) It is claimed that a large corporation discriminates against its women employees in its promotion practices. Over many years, the mean time before first promotion for its male employees has been 3 years. A random sample of 20 females, who had worked there many years, showed a mean time of 3.8 years before first promotion, with s=1.2 years. Using a level of significance of 5%, see if the data support the claim. (2) The average IQ of a group of researchers is quoted to be 260. Thinking that this figure is too large, a consulting firm tested a random sample of 8 researchers and found that the average IQ was 250 with s=8. Test at a level of significance of 1%. (3) A claim is made that the mean height of police officers is 5 feet 11 inches. To test whether this claim is true or not, a random sample of 25 police officers was gathered. This sample had a mean height of 5 feet 10 inches with s=3 inches. Test at the 5% significance level. (4) To test whether or not there is a difference between the mean grade point averages of male math majors and female math majors at a certain university, 2 random samples were gathered. For the 35 males we find that the sample mean is 3.1 with s=0.2. For the 20 females, the sample mean is 3.2 with s=0.15. Test at a 1% level of significance. (5) Are “krispy toasters” quicker than “No-burn toasters” at the 1% significance level, if the times it took to toast a slice of bread were as follows: No-Burn: 60,55,70,65,80 seconds Krispy: 70,65,65,60,60 seconds ? (6) The mean score on a standardized psychology test is supposed to be 50. Believing that a group of psychologists will score higher, we test a random sample of 11 psychologists. Their mean score is 45 with s=3. Test at a 1% level of significance. (7) On field trips, science classes collect toads in a swamp. In June, 50 toads were caught with a mean weight of 1.1 ounces and with s=0.05 ounce. In August 25, toads were caught with a mean weight of 2.1 ounces and s=0.07 ounce. Does this indicate at the 1% significance level that August toads are heavier than June toads? (8) Is there a statistically significant difference between the bowling averages of male nurses and those of businessmen, if last year’s league play produced the following data: 10 male nurses averaged 180 with s=10, and 15 businessmen averaged 170 with s=10? Use 5% level of significance. (9) To see whether there is a statistically significant difference between the age of owners of convertibles and the age of owners of sedans, an advertising agency found that 15 convertible owners had an average age of 29.2 years with s=5, and 35 sedan owners had an average age of 24.8 years with s=8. Test at a 5% level of significance. (10) An astronomer is testing the claim that the mean brightness of a certain star is now more than 30 units. The astronomer is able to get 6 readings on the star during an experiment as shown in the table. Using a 1% level of significance, does this indicate a new mean brightness of more than 30? Reading Brightness 1 30 2 30 3 29 4 31 5 32 6 33