Question

Researchers studied the compression strength in lbs of 12-oz aluminum cans. A simple random sample of 35 aluminum cans filled with cola (which has more carbonation) had a sample mean compression strength of 554 lbs and a sample standard deviation of 15 lbs. A simple random sample of 30 aluminum cans filled with strawberry soda had a sample mean compression strength of 540 lbs and a sample standard deviation of 21 lbs. At the 0.05 significance level, perform a hypothesis test to determine if the mean compression strength, Mys of aluminum cans filled with cola is more than the mean compression strength, My, of aluminum cans filled with strawberry soda. 1. Select the appropriate null and alternate hypotheses. Онон, = Д., Н, 4 р. Онон, = Д., Н, , > Ну OH, Hy>H2, H, H4 = H2 OH, My > M2, H₂ H <H2 OH, Hy = H2, H, MyZH2 OHHy = H2, H, My + H2 2. Find the value of the test statistic. Round to three decimal places. 3. Find the P-value. Round to four decimal places.

Answer 1

The problem is to test to determine the mean compression Strength, 44, of alumioum cans filled with cola is more than the meas compression strength, le of aluminum cans filled with strawberry seda 1) Hypothesis Hoel, = 42 Hr iel, uz 35 Letni be the size of sample of aluminum cans filled with Soda na be the size of sample of aluminum cans filled strawberry sodas be the mean of sample 1 = 554 lbs be the mean of sample 2 = 540 lbs s, and Sa be the sample Standard deviation of Sample 1 and 2 respectively sia is lbs S, = 21 lbs 1x1x in

In this problem the sample size is large so weuse we use Z test for means Z = 2) Test Statistic X2 si 52² + ni he S54 - 540 (15) (21)² 35 30 + - 14 4.5965 = 3,0457 Level of significance a = 0.05 3) He calculate P-value using excel p-value =1-NORM SDIST (2) =1-NORM SDIST(3,0451) - 1 - 0, 9988 IP-value - 0,0012 M 3.0457 P-value <a Hence reject. Ho Conclusion ! Reject the pull bypothesis. The mean com pression strength el of aluminum cans filled with cola is more than the mean compression strength to of aluminum cans filled with Strawberry soda j.e. el > 112