This is from my Statistics Homework and I answered all of them, can someone plea

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This is from my Statistics Homework and I answered all of them, can someone please double check my answers and if I missed one then explain what is/how to get the correct answer?

1. An experimenter wants to conduct a hypothesis test on a claim that there was no difference between two population means. That is, H0: 1 – 2 = 0. The experimenter randomly selected 10 items from the first population and 10 items from the second population. The population variances are assumed to be known. Specifically, the variance of the first population is 25 and the variance of the second population is 36. If you were to conduct the test for the experimenter, which case from Chapter 10 would this problem fall under or represent?

A. Case I – Use z statistic with known population variances
B. Case II – Use t statistic, assuming variances are unknown but equal
C. Case III –Use t statistic, assuming variances unknown and unequal
D. Case IV – Use paired t test

Choose answer A

2. A two-sample t test is going to be carried out where it is assumed that the population variances are unknown but assumed equal. The first sample of 30 items were chosen and measured. For this first sample, an average response of 125 with a sample variance of 25 was found. The second sample of 40 items were chosen and measured. This second sample had an average response of 132 with a sample variance of 16. What is the pooled standard deviation for this problem? (rounded to second place after the decimal)

A. 4.45 B. 19.84 C. 413.37 D. 20.33

Choose answer A

3. An experimenter wants to conduct a hypothesis test on a claim that there was no difference between two population means. That is, H0: 1 – 2 = 0. Which of the following 95% confidence intervals on the difference, 1 – 2, would lead to rejection of the null hypothesis at the 5% level of significance?

A. (-14.2, 28.7)
B. (-2.4, 20.5)
C. (3.5, 5.6)
D. None of the above

Choose answer C

4. Fifteen people will be enrolled in a four-week foreign language course. On the first day, the instructor gives the students an exam to determine how much they already know. At the end of the four weeks, the instructor gives the students the same exam again. From the exam scores, the instructor wants to determine if taking the course has significantly increased the students’ foreign language ability. Which of the four cases in Chapter 10 does this problem fall under or represent?

A. Case I – Use z statistic with known population variances

B. Case II – Use t statistic, assuming variances are unknown but equal

C. Case III –Use t statistic, assuming variances unknown and unequal

D. Case IV – Use paired t test

Choose answer D

5. The following output from a two-sample t-test using Minitab was obtained for a particular problem:
Two-sample T for side_side
Age_Group N Mean StDev SE Mean

elderly 9 22.2 10.3 3.4
young 8 15.13 3.91 1.4
Difference = mu (elderly) - mu (young)
Estimate for difference: 7.10
95% CI for difference: (-1.13, 15.32)
T-Test of difference = 0 (vs not =): T-Value = 1.92 P-Value = 0.083 DF = 10
For which of the following levels of significance would you reject the null hypothesis?

A. 0.01
B. 0.05
C. 0.10
D. None of the above.

Choose answer C

Explanation / Answer

1) A. Case I – Use z statistic with known population variances

2) Pooled std. dev is = Sqrt ((n1-1)*S12 +(n2-1)*S22)/(n1+n2-2))

= Sqrt (((29*25)+(39*16))/68)

= 4.45

3) (3.5, 5.6)

4) Case IV – Use paired t test

5) 0.10

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