Show All work please , thank you David Anderson has been working as a lecturer a
ID: 3156452 • Letter: S
Question
Show All work please , thank you David Anderson has been working as a lecturer at Michigan State University for the last three years He teaches two large sections of introductory accounting every semester. While he uses the same lecture notes in both sections. his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores. David decides to carry out a formal test to validate his hunch regarding the difference in average scores. In a random sample of 22 students in the first section, he computes a mean and a standard deviation of 84.4 and 12.8. respectively In the second section, a random sample of 25 students results in a mean of 61.9 and a standard deviation of 1 22. Sample 1 consists of students in the first section and Sample 2 represents students in the second section. Construct the null and the alternative hypotheses to test David's hunch. H_0: mu_1 - mu_2 GE 0: H_A mu_1 - mu_2 0 H_0: mu_1 - mu_2 = 0: H_A: mu_1 - mu_2 notequal 0 Calculate the value of the test statistic (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Test statistic What assumption regarding the population variances is used to conduct the test? Known population standard deviations Unknown population standard deviations that are equal Unknown population standard deviations that are not equal Implement the test at a = 0.05 using the critical value approach. Do not reject H_0: scores are not higher in the first section Reject H_0: scores are not higher in the first section. Reject H_0: scores are higher in the first section. Do not reject H_0: scores are higher in the first section.Explanation / Answer
a) Here we have to test the hypothesis that,
H0 : mu1-mu2 = 0 Vs H1 : mu1-mu2 0
where mu1 and mu2 are two population means.
Option d) is correct.
b-1) We have to find test statistic.
Here we use two sample t-test because sample sizes are small and population standard deviations are unknown.
Before that we have to test equality of variances.
The hypothesis for the test is :
H0 : Variances are equal.
H1 : Variances are not equal.
Assume alpha = 5% = 0.05
X1bar = 84.4
X2bar = 81.9
sd1 = 12.8
sd2 = 12.2
n1 = 22
n2 = 25
This we can done using TI-83 calculator.
steps :
STAT --> TESTS --> D:2-SampFTest --> ENTER --> HIghlight on stats --> ENTER --> Input all the values --> alternative : select --> ENTER --> Calculate --> ENTER
Test statistic F = 1.10
P-value = 0.8147
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : Variances are equal.
We use pooled variances.
Two sample t-test in TI_83 calculator.
steps :
STAT --> TESTS --> 4:2-SampTTest --> ENTER --> Highlight on Stats --> ENTER --> Input all the values --> select alternative "" --> Pooled : yes --> ENTER --> Calculate --> ENTER
The test statistic t = 0.685
P-value = 0.4968
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is sufficient evidence to say that two population means are not equal.
b-2) Unknown population standard deviations that are equal.
Option b) is correct.