Question

A manufacturer must test that their bolts are 2.00 cm long when they come off the assembly line. If the bolts are either too long or too short, then the machines must be recalibrated. After sampling 100 randomly selected bolts off the assembly line, the sample mean is calculated to be 1.90 cm. Suppose that the population standard deviation is known to be 0.50 cm. Is there sufficient evidence to show that the manufacturer needs to recalibrate the machines at the 0.001 level of significance.
    a. State the null and alternative hypothesis
    b. Identify which distribution to use for the test statistic. If applicable, calculate the number of degree of freedom, if not applicable then state so.
    c. Compute the value of the test statistic z, t, or x^2
    d. Compute the p-value associated to the test statistic.
    e. Choose whether or not to reject the null hypothesis.

Answer 1