What hypothesis testing procedure should you use to answer these questions? Assume all samples are simple random samples, and assume α = 0.05 if it isn’t specified.
A company wishes to purchase a new machine to produce ball bearings since the new machine is faster, and so will produce more ball bearings than the old machine. They decide to purchase the new machine only if the mean strength of the bearings is not less than the old machine. The old machine produces bearings that can withstand 400 lbs per square inch. The company is allowed to test the new machine for a day, so they produce 100 ball bearings under the usual operating conditions on the new machine. They find that the average strength to be approximately 398.5 lbs per square inch and the SD to be about 5 lbs per square inch. The sample distribution does not look normal. Should the company purchase the new machine, at α = 0.05?
Question 22 options:
One sample z-test for the population mean.
Two sample z-test for the population means.
One sample z-test for proportions.
Two sample z-test for proportions.
One sample t-test for the population mean.
None of our hypothesis tests fit.
The hypothesis test that should be used to answer this question is a one sample t-test for the population mean.
In this scenario, the company wants to compare the mean strength of the bearings produced by the new machine to the mean strength of 400 lbs per square inch produced by the old machine. Since the sample size is relatively small (n = 100) and the population standard deviation is unknown, a t-test is appropriate.
The null hypothesis (H0) would be that the mean strength of the bearings produced by the new machine is less than or equal to 400 lbs per square inch. The alternative hypothesis (Ha) would be that the mean strength is greater than 400 lbs per square inch.
The test statistic would be calculated using the formula:
t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(n))
The critical value for a one-tailed t-test with α = 0.05 and 99 degrees of freedom (n-1) can be obtained from a t-table or a t-distribution calculator.
If the test statistic is greater than the critical value, the company should purchase the new machine. If the test statistic is less than or equal to the critical value, the company should not purchase the new machine.