Please help and show work, not sure where I am going wrong! Attempt 2 Question 7

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Please help and show work, not sure where I am going wrong!

Attempt 2 Question 7 of 8 Attempt 1 Suppose that a manufacturing process has resulted in an average production time of 290 min with a standard deviation o 58 min for the last two years. Recently, a sales representative suggested that production time could be decreased by incorporating a new machine into the process. The plant manager agreed to test the machine for 70 days (the sample size is n 70 days) and will use the average time for production over those 70 days to determine whether the inclusion of the machine decreases production time. The manager plans to conduct a test of Ho: Au 290 H1 :u 290 where Au is the mean production time after incorporating the new machine. The plant manager wants to know the power of this test to correctly reject the null hypothesis at a significance level a 0.05 if the actual mean production time after incorporating the new machine is 265 minutes. Computing power by hand requires two steps The first step is to use a significance level of a 0.05, the population standard deviation of o 58, the sample size of n 70, and the assumed population mean of u J 290 to determine the maximum sample mean that will reject the null hypothesis. Round your answer to the nearest tenth of a minute. min x In the second step, find the power of the test by first assuming that the actual mean is 265 minutes. Then, compute the a the critical region found in the first step. Leave the boundaries of the critical region probability of getting sample mean in rounded to one decimal place in your calculation, and give your answer in decimal form precise to at least two decimal places

Explanation / Answer

for std error =58/sqrt(70) =6.93

hence the test stat z=(X-mean)/std error fro which critical value at 0.05 level =-1.64485

hence -1.64485>(X-290)/6.93

X<278.5973

b)here for left 5%; rejection region X<278.5973

hence power =P(X<278.5973) =P(Z<(278.5973-265)/6.93)=P(Z<1.9614)=0.9751

pls check and revert

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