Homework 12: Additional Problems

Assume that each of the samples below are a random sample from a population that is approximately normally distributed.

For each of the following problems:

  1. State the claim in terms of an equality/inequality involving the population mean.
  2. Determine whether the claim corresponds to a null or alternative hypothesis.
  3. Determine the complementary hypothesis to the claim.
  4. State the null and alternative hypotheses.
  5. Determine the type of evidence, involving the sample mean, which would be evidence against the null hypothesis.
  6. Draw the density curve for \(T\) under the null hypothesis.
  7. Determine the observed value of the \(T\)-statistic \(t_{\text{obs}}\) from the sample properties, and indicate where this value falls under the density curve.
  8. Determine whether the observed \(T\)-statistic gives evidence against the null.

Worked Example

You can find a worked example here.

Problems

1. Claim: The population mean is less than 55.

Sample Properties: \(n\) = 33, \(\bar{x}\) = 51.49, \(s_{X}\) = 10.04

2. Claim: The population mean is at least 11.

Sample Properties: \(n\) = 33, \(\bar{x}\) = 17.42, \(s_{X}\) = 10.63

3. Claim: The population mean is at most 64.

Sample Properties: \(n\) = 6, \(\bar{x}\) = 57.27, \(s_{X}\) = 64.41

4. Claim: The population mean is more than 60.

Sample Properties: \(n\) = 28, \(\bar{x}\) = 60.82, \(s_{X}\) = 5.52

5. Claim: The population mean is at most 81.

Sample Properties: \(n\) = 34, \(\bar{x}\) = 71.24, \(s_{X}\) = 21.73