Is there evidence to support the claim that this particular diet- modification p

Question

Is there evidence to support the claim that this particular diet- modification program will result in a mean weight loss of at least 10 pounds? Use alpha = 0.05. A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 60, 139.7 kilometers and 3645.94 kilometers. Can you conclude, using alpha = 0.05, that the standard deviation of tire life is less than 4000 kilometers? State any necessary assumptions about the underlying distribution of the data. Find the P-value for this test.

Explanation / Answer

Question 6

Mean = 60139.7 Km

Standard Deviation = 3655.94 Km

Null Hypothesis : H0: = 4000 Km

Alternative Hypothesis : Ha : < 4000 Km

Necessary assumptions

(i) The sample is a simple random sample.

(ii) The distribution is normal for tire life.

Test Statistic:

X2= (n-1)s2/ 02 = (16-1)* (3655.94)2 /(4000)2 = 12.53

for dF = 15 and X2critical= 7.261

so X2   > X2criticalwe can not reject the null hypothesis and can say that standard deviation is not less than 4000 km.

so P - value = cdf (0, 12.53, 15) = 0.3615

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