Question

Duta on the weights (b) of the conterts of cans of det soda versst the contents of cens of the regbar venion of the soda is summarirad o the right Uve a 0.05 signilicance level for both parts, Assume that the tandard deviatons of both are equal. 1. Tect the clam that the oortants of nas of det loda have woights wih a mean that in lese then the mean for the regular soda What are the relli and allematie typolheses? A. He−Fin 1 +μ 2 18. H 0 −μ 15 P 2 H :μ1>H2 c. M 6 v 1 2μ 2 D. Hb 2 Hi 1 =H 2 H 4 :H 4 The vest rtutstc, t, in (Phound to two decimal places as needed) The Prakus is (Pocund to thee decimal places at needed) Stite the conctuing bor the inet. State the conclusion for the test A. Fail to reject the null hypohesis. There is not suticiert evidence to support the claim that the cans of det soda have mean woights that are lower than the mean welght for the regular gods B. Roject the nuil hypothesis. There is sufficient evidence to support the claim that the cars of diat soda have mean weights that are lowor than the mean weight for the regular soda. C. Rejec the nul bypothesis. There is nof sufficient evidence to support the elaim that the cans of diet soda have mean weighis that are lower than the mean weight for the regular soda. D. Fail to reject the min hypothesis. There is wutficient evidence to support the claim that the cans of diet seda have mean weights that are

Answer 1

The student's question involves setting up hypotheses for a hypothesis test to compare the mean weights of diet versus regular soda. The proper hypotheses state that the mean weight of diet soda is equal to or less than the weight of regular soda, and the conclusion is based on the calculated p-value in relation to the significance level.

Step-by-step explanation:

The question appears to be about a hypothesis test for comparing the means of two normally distributed populations, specifically regarding the weights of diet soda versus regular soda. The null hypothesis (H₀) should state that there is no difference between the mean weights, while the alternative hypothesis (H₁) should propose that the mean weight of diet soda is less than that of regular soda.

The correct hypotheses would be:

• H₀: μ₁ = μ₂ (The mean weight of diet soda is equal to that of regular soda.)
• H₁: μ₁ < μ₂ (The mean weight of diet soda is less than that of regular soda.)

To perform the test, we would calculate the test statistic (t-value) and the corresponding p-value. Depending on the p-value and the significance level (α = 0.05), we would then either reject or fail to reject the null hypothesis. A low p-value (less than 0.05) would indicate sufficient evidence to reject the null hypothesis and accept the alternative hypothesis that the mean weight of diet soda is less than that of regular soda. Conversely, a p-value greater than 0.05 would lead to a failure to reject the null hypothesis, suggesting insufficient evidence to support the claim that diet soda cans have a lower mean weight.