Let's work through this step by step:

Part (a) Hypotheses:

• Null hypothesis $H_0$: The null hypothesis represents the assumption that there is no difference from the current reported value, which is 35 minutes. This is the "status quo" hypothesis. $H_0: \mu = 35 \text{ minutes}$

• Alternative hypothesis $H_1$: The alternative hypothesis reflects the suspicion or the idea that the mean shopping time is different from 35 minutes. Since it's a two-tailed test (executives believe it could be either greater or less than 35), the alternative hypothesis would be: $H_1: \mu \neq 35 \text{ minutes}$

Part (b) Type of Error:

• If the consultant decides not to reject the null hypothesis but the true mean is different from 35 minutes, she could be making a Type II error.
  • A Type II error occurs when the null hypothesis is not rejected, even though it is false.

Part (c) Type II Error Description:

• Suppose the true mean shopping time is 42 minutes.
• A Type II error would involve failing to reject the null hypothesis when the null hypothesis is false. Specifically, this error would be failing to reject the hypothesis that $\mu = 35$ when, in fact, $\mu = 42$.

Putting it all together:

• (a) $H_0: \mu = 35$ minutes, $H_1: \mu \neq 35$ minutes.
• (b) The consultant might be making a Type II error.
• (c) A Type II error would be failing to reject the hypothesis that $\mu = 35$ minutes when, in fact, $\mu = 42$ minutes.

Would you like more details on any part of the explanation?

Related questions:

1. What is the difference between Type I and Type II errors?
2. How does sample size affect Type II error?
3. What are the consequences of a Type II error in real-life decision-making?
4. How do you calculate the test statistic for this hypothesis test?
5. What is the role of the standard deviation in this test?

Tip: Increasing the sample size can reduce the likelihood of making a Type II error by increasing the power of the test.