(f) Apply the critical value approach to test the hypotheses developed in (d): (

Question

(f) Apply the critical value approach to test the hypotheses developed in (d): (Compute the critical value and make conclusion in the context of the problem.) Let a be 1 %. (g) Use the sample to construct a 98% confidence interval estimate for the proportion of defective switches produced. Interpret the confidence interval in the context of the problem. (h) Refer to the confidence interval obtained in (g). Can we conclude with 98% confidence that the population defective rate is above 0.8%? Briefly explain your answer. A courier service advertises that its average delivery time is less than 6.5 hours for local deliveries. A random sample of 14 deliveries to an address than 6.5 hours for local deliveries. A random sample of 14 deliveries to an address across town was recorded. These data are shown below (in hours). 8.21 3.98 4.25 5.48 4.78 6.68 7.11 7.35 6.45 2.95 7.23 4.92 3.95 5.35 (a) Is there sufficient evidence to support the courier's advertisement, at the 5% level of significance? Apply the critical value approach.

Explanation / Answer

2) here null hypothesis: mean>=6.5

alternate hypothesis: mean<6.5

here test stat  t=(X-mean)/std error =-2.0938

for above at 13 degree of freedom ; pvalue =0.0282 .

as p value is less then 0.05 level ; we can reject null hypothesis, and have sufficient evidence to support the courier's advertisement.

X 8.21 3.98 4.25 5.48 4.78 6.68 7.11 7.35 6.45 2.95 7.23 4.92 3.95 5.35 mean(X) 5.621 std deviation(S) 1.571 std error =S/(n)1/2 0.4200

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