Dala on the weights (Ib) 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. Diet Regular P2 37 0.78651 lb 0.00449 lb 0 80884 lb 0.00748 Ib a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? O A. Ho H =P2 O B. Họ: H "P2 H,: H 2 OC. Ho H, Ha O D. Ho: H =2 The test statistic, t, is. (Round to two decimal places as needed.) The P-value is. (Round to three decimal places as needed.) State the conclusion for the test. OA. 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. 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. OC. 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. OD. 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. b. Construct a confidence interval appropriate for the hypothesis test in part (a). Oib

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Data on the weights of the contents of cans of diet soda versus the contents of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples from normally distributed populations, and do not assume that the population standard deviations are equal.

Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the reqular 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.
Diet
Regular
n
37
0.78651 Ib
0.00449 Ib
0.80884 Ib
0 00748 Ib
a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.
What are the null and alternative hypotheses?
O A. Ho: H1 =H2
O B. Ho: H1 =H2
H,: H, > H2
OC. Ho: H, H2
O D. Ho: H1 =H2
H,: H <P2
The test statistic, t, is . (Round to two decimal places as needed.)
The P-value is |. (Round to three decimal places as needed.)
State the conclusion for the test.
O A. 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.
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. 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 D. 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.
b. Construct a confidence interval appropriate for the hypothesis test in part (a).
Ib < H, - H2 *L Ib
(Round to three decimal places as needed.)
Does the confidence interval support the conclusion found with the hypothesis test?
because the confidence interval contains

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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