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 0.01 significance level for both parts. Diet Reqular μ2 26 0.81485 Ib 0.00755 lb 26 0.78439 Ib 0.00441 Ilb 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? The test statistic, t, is (Round to two decimal places as needed.) The P-value isRound 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 ○ 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). (Round to three decimal places as needed.) Does the confidence interval support the conclusion found with the hypothesis test? because the confidence interval contains

Answer 1

Null hypothesis. H. : M 2,02 Alternative hypothesis, H, : μ1 < μ2 Level of significance, α = 0.01 The test is one tail (left tail Calculate the test statistic: By using the excel software to determine the test statistic and p-value with the help following procedure: 1. Enter the data in excel sheet. 2. Click on add ins in the excel tool bar 3. Choose hypothesis tests-> compare two independent groups 4. In hypothesis compare two independent groups dialog box, choose data input and enter the input range of sample 1 and sample 2. 5. Enter hypothesis difference is 0-altemative hypothesis less than-> test( un equal 99% confidence interval. variance) Click ok. 6. To get the required output is given below:

Hypothesis Test: Independent Groups (t-test, unequal variance) diet Reqular 0.78439 0.81485mean 0.0044 0.00755 std. dev 26 n 26 40 df 0.0304600 difference (diet - Regular) 0.0017148 standard error of difference 0 hypothesized difference -17.76 t 0.000 p-value (one-tailed, lower) 0.035 confidence interval 99.% lower -0.026 confidence interval 99% upper 0.005 margin of error From the above output, The test statistic is -17.76 The p-value is 0.000.

Compare the p value with α. Reject Ho, if psa otherwise do not reject H. Since the p-value is less than the significance level, reject the null hypothesis at 1% level of significance conclusion: Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of soda have mean weights that are lower than the mean weight for the regular diet. b) The 99% confidence interval for the difference of means is, -0.035 < ц-4 <-0.026 Yes, the confidence interval support the conclusion found with the hypothesis test. Since the confidence interval does not contain the null value then the null hypothesis can be rejected.