Question

A company that receives shipments of batteries tests a random sample of nine of them before agreeing to take a shipment. The company is concerned that the true mean lifetime for all batteries in the shipment should be at least 40 hours. From past experience, it is safe to conclude that the population distribution of lifetimes is normal with a standard deviation of 3 hours. For one particular shipment, the mean lifetime for a sample of nine batteries was 38.7 hours. a. Test, at the 1% level, the null hypothesis that the population mean lifetime is at least 40 hours. b. Find the power of a 1%-level test when the true mean lifetime of batteries is 39 hours. Click the icon to view the standard normal distribution table. C. Reject H0 if (x-bar - mu0) / (sigma / sqrt(n)) < -z_alpha Determine the value for -z_alpha, z_alpha, or +/- z_alpha/2 as appropriate for this test. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Calculate the test statistic. (x-bar - mu0) / (sigma / sqrt(n)) = (Round to one decimal place as needed.) State the conclusion of this test. Reject the null hypothesis. There is not sufficient evidence to conclude that the population mean lifetime is less than 40 hours. b. The power of this test when the true mean lifetime of batteries is 39 hours is . (Round to four decimal places as needed.)

          A company that receives shipments of batteries tests a random sample of nine of them before agreeing to take a shipment. The company is concerned that the true mean lifetime for all batteries in the shipment should be at least 40 hours. From past experience, it is safe to conclude that the population distribution of lifetimes is normal with a standard deviation of 3 hours. For one particular shipment, the mean lifetime for a sample of nine batteries was 38.7 hours.
a. Test, at the 1% level, the null hypothesis that the population mean lifetime is at least 40 hours.
b. Find the power of a 1%-level test when the true mean lifetime of batteries is 39 hours.
Click the icon to view the standard normal distribution table.
C. Reject H0 if (x-bar - mu0) / (sigma / sqrt(n)) < -z_alpha
Determine the value for -z_alpha, z_alpha, or +/- z_alpha/2 as appropriate for this test.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Calculate the test statistic.
(x-bar - mu0) / (sigma / sqrt(n)) = (Round to one decimal place as needed.)
State the conclusion of this test.
Reject the null hypothesis. There is not sufficient evidence to conclude that the population mean lifetime is less than 40 hours.
b. The power of this test when the true mean lifetime of batteries is 39 hours is .
(Round to four decimal places as needed.)

A company that receives shipments of batteries tests a random sample of nine of them before agreeing to take a shipment. The company is concerned that the true mean lifetime for all batteries in the shipment should be at least 40 hours. From past experience, it is safe to conclude that the population distribution of lifetimes is normal with a standard deviation of 3 hours. For one particular shipment, the mean lifetime for a sample of nine batteries was 38.7 hours.
a. Test, at the 1% level, the null hypothesis that the population mean lifetime is at least 40 hours.
b. Find the power of a 1%-level test when the true mean lifetime of batteries is 39 hours.
Click the icon to view the standard normal distribution table.
C. Reject H0 if (x-bar - mu0) / (sigma / sqrt(n)) < -zalpha
Determine the value for -zalpha, zalpha, or +/- zalpha/2 as appropriate for this test.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Calculate the test statistic.
(x-bar - mu0) / (sigma / sqrt(n)) = (Round to one decimal place as needed.)
State the conclusion of this test.
Reject the null hypothesis. There is not sufficient evidence to conclude that the population mean lifetime is less than 40 hours.
b. The power of this test when the true mean lifetime of batteries is 39 hours is .
(Round to four decimal places as needed.)

Added by Deborah R.

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