Question

Diet Regular Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Cixon 21 0.78134 lb 0.00443 lb H2 21 0.80778 lb 0.00749 lb The test statistic, T, IS – 13.92 . (Round to two decimal places as needed.) The P-value is 0. (Round to three decimal places as needed.) State the conclusion for the test. O A. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. O C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. D. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. b. Construct a confidence interval appropriate for the hypothesis test in part (a). 10<441 - H26 (Round to three decimal places as needed.)

Answer 1

Solution :

The statistic software output for this problem is:

Two sample T summary hypothesis test: P: Mean of Population 1 P2 : Mean of Population 2 H.-2: Difference between two means HP - H2 = 0 HA: P.--2=0 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value H-2 -0.02644 0.0018989345 32.457127 -13.923597 <0.0001

Two sample T summary confidence interval: Pi : Mean of Population 1 2 : Mean of Population 2 - - - : Difference between two means (without pooled variances) 99% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit P. 2 -0.02644 0.0018989345 32.457127 -0.0316355 -0.0212445

(a)

Test statistic = -13.92

P-value = 0.0000

(b)

A confidence interval is :

-0.032 lb <  
μl – μ2
< -0.021 lb