Two sample intervals for means

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Jenny wants to compare the amount of weight that people lose at her gym using two popular, non-overlapping weight-loss programs, Shred It and Burn It. She begins by randomly sampling

35

of the approximately

100

people who used Shred It and finds that their average weight loss was

10

kg

with a standard deviation of

3.5

kg

. She then randomly samples

35

of the approximately

100

people who used Burn It and finds that their average weight loss was

7

kg

with a standard deviation of

5.7

kg

. Jenny then uses this information to construct a confidence interval estimate for the difference in the average amount of weight that people lose at her gym using the two weight-loss programs.

Which statement about Jenny’s confidence interval is true?

(Choice A)
Jenny's confidence interval will be invalid because she did not randomly assign her subjects to the two treatments .
(Choice B)
Jenny's confidence interval will be invalid because she may not reasonably approximate the standard error of the difference in sample means using the formula $S E_{{\bar{x}}_{1} - {\bar{x}}_{2}} = \sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}$ ‍.
(Choice C)
Jenny's confidence interval will be invalid because she may not reasonably assume that the sampling distribution of the difference in sample means is approximately normal.
(Choice D)
Jenny's confidence interval will be invalid because she does not know the the standard deviations of the amount of weight loss ( $σ_{1}$ ‍ and $σ_{2}$ ‍) from everyone at her gym that uses Shred It and Burn It.
(Choice E)
Jenny's confidence interval will be valid because all of the conditions for a two sample interval for a difference between two means are met.

Staging content lifeboat

Course: Staging content lifeboat > Unit 13

Problem