Question

1. Confidence interval for the difference between the two population means.
(Assume that the two samples are independent simple random samples selected from normally distributed populations.)

A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following summary statistics:

College A	College B
= 3.1125	= 3.4385
s1 = 0.4357	s2 = 0.5485
n1 = 8	n2 = 13

  
Construct a 95% confidence interval for μ₁ – μ₂, the difference between the mean GPA of students in college A and the mean GPA of students in college B .

Select one:

A.-0.78 < μ₁ – μ₂< 0.13

B, -0.84 < μ₁ – μ₂< 0.19

C, -0.80 < μ₁ – μ₂< 0.15

D, -0.75 < μ₁ – μ₂< 0.18

2.

A researcher was interested in comparing the response times of two different cab companies. Companies A and B were each called at n = 36 randomly selected times. The calls to company A were made independently of the calls to company B. The response times were recorded and the summary statistics were as follows:

	Company A	Company B
Mean response time	12.3 mins	15.0 mins
Standard deviation	2.8 mins	4.2 mins

Find the margin of error, E, for a 98% confidence interval that can be used to estimate the difference between the mean resting pulse rate of people who do not exercise regularly and the mean resting pulse rate of people who do. Round your answer to two decimal places.
(Note: Use Table A-3 for the critical value needed in the formula)

Answer 1

The above is t table which we will use ahead

Hope this helps.
Thank You