Question

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 0.05 significance level for both parts. Diet Regular H2 25 x 25 0.78225 lb .00449 lb 5 0.80137 lb 0.00744 lb The test statistic, t, is -11.00. (Round to two decimal places as needed.) 0 The P-value is 0.000. (Round to three decimal places as needed.) State the conclusion for the test. O A. 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. GB. 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. Reject the null hypothesis. There is sufficient evidence to support the aim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. CD. b. Construct a confidence interval appropriate for the hypothesis test in part (a). <H1-H2b (Round to three decimal places as needed.) Enter your answer in the edit fields and then click Check Answer. . part remaining Wear All

Answer 1

Let , $\mu_1$ be the population mean of diet and $\mu_2$ be the population of regular.

Hypothesis :
Hopi = pz
VS
HQ: M1 <H2

Since , the population standard deviations are not equal.

Therefore , use the Z-test.

a)

The test statistic is ,

X-X。 → N(0,1) +

0.78225 - 0.80137 = -11.00 0.0094492 + 0,074

The P-value is ,

P-value = ; From normal probability integral table

P(Z > ZSTAT) = P(Z > 11.00) = 0.0000

Decision : Here , P-value < 0.05

Therefore , reject Ho

Conclusion : Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower that the mean weight for the regular soda.

b)

The 95% confidence interval is ,

| (Xi - X2) + Za/21 +

(0.78225 -0.80137) 4 Zo.05/2 1 10.004492 5 十 0.007442 25

ΣΤ000 * 96'ΙΞ Ι6ΙΟ'0-

-0.019140.0033

-0.022 < μι - μ2 < -0.016

Here , the value does not lies in the 95% confidence interval.

11- 2 = 0

Therefore , reject Ho.