Let's break this problem down part by part:

Part (a) Null and Alternative Hypotheses

In hypothesis testing, the null hypothesis (H₀) usually represents the statement we assume to be true until evidence suggests otherwise. The alternative hypothesis (H₁) is what we aim to support with the test.

• The executives have reason to believe that the mean shopping time, μ, is less than 35 minutes.
• The current belief is that the mean shopping time is μ = 35 minutes.

Thus, the hypotheses should be formulated as follows:

• Null hypothesis (H₀): μ = 35 minutes
  (The mean shopping time is 35 minutes.)

• Alternative hypothesis (H₁): μ < 35 minutes
  (The mean shopping time is less than 35 minutes.)

Part (b) Type of Error

When the consultant rejects the null hypothesis, there are two possible errors that can occur in hypothesis testing:

• Type I error (False Positive): This occurs when we reject a true null hypothesis.
• Type II error (False Negative): This occurs when we fail to reject a false null hypothesis.

In this case, if the consultant rejects the null hypothesis (μ = 35 minutes), but in reality, μ is still 35 minutes, she would be making a Type I error. That is, she would be rejecting a true null hypothesis.

Part (c) Type I Error Description

Suppose the true mean shopping time is indeed 35 minutes, which aligns with the null hypothesis. If the consultant rejects the null hypothesis (believing μ < 35 minutes), she would be committing a Type I error.

Here’s how to fill in the blanks:

• A Type I error would be rejecting the hypothesis that μ = 35 minutes when, in fact, μ = 35 minutes.

This means she mistakenly concludes that the mean shopping time is less than 35 minutes when, in fact, it is still 35 minutes.

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Let me know if you'd like more details or have any questions.

Here are some relative questions to further understand the topic:

1. How would you calculate the test statistic for this hypothesis test?
2. What is the significance level (α) in this context, and how does it relate to Type I error?
3. How could a Type II error occur in this test?
4. What assumptions must be made about the distribution of shopping times to use a t-test here?
5. How could the supermarket executives reduce the risk of making a Type I error?

Tip: In hypothesis testing, always define the null and alternative hypotheses clearly before conducting the test, and consider the implications of both Type I and Type II errors.