A carpenter is making doors that are 2058 millimeters tall. If the doors are too

Question

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of46

doors is taken, and it is found that they have a mean of 2069 millimeters. Assume a population standard deviation of

25. Is there evidence at the0.02level that the doors are too long and need to be trimmed?

State the null and alternative hypotheses

Find the value of the test statistic. Round your answer to two decimal places.

Find theP-value of the test statistic. Round your answer to four decimal places.

Identify the level of significance for the hypothesis test.

Explanation / Answer

null hypothesis:mean =2058

alternate hypothesis: mean>2058

level of significance =0.02

here std error =std deviation/(n)1/2 =3.686

hence test stat z=(X-mean)/std error =(2069-2058)/3.686 =2.9842

for above test stat p value=0.0014

as p vlaue is less then 0.02 level ; we reject null hypothesis, and conclude that there is evidence at the0.02level that the doors are too long and need to be trimmed

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