The mean work week for engineers in start-up companies is claimed to be about 58

Question

The mean work week for engineers in start-up companies is claimed to be about 58 hours with a standard deviation of 4 hours. Kara, a newly hired engineer hopes that it's not (she wants it to be shorter). She asks 10 engineers in start-ups for the lengths of their mean work weeks. Their responses are 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.

The null hypothesis (or company claim), in symbols, is =

If the claim is correct, what is the probability that a sample mean would be as low as Kara's mean? ______%

Explanation / Answer

null hypothesis :Ha": = 58

std error =std deviation/(n)1/2 =4/(10)1/2 =1.2649

sample average =57

tehrefore test stat z=(X-mean)/std error =(57-58)/1.2649 =-0.7906

for abvoe test stat p value =0.2146

probability that a sample mean would be as low as Kara's mean =21.46%

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