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Refer to Exercise 9.16. Explain what each of the following would mean.

(a) Type I error.

(b) Type II error.

(c) Correct decision.

Now suppose that the results of carrying out the hypothesis test lead to the rejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean lactation period of grey seals.

(d) equals 23 days.

(e) differs from 23 days.

Short Answer

Expert verified

(a) Rejecting a Null Hypothesis, when it is true.

(b) Rejecting a Null Hypothesis, when H0is false.

(c) If the true null hypothesis is not rejected or a false null hypothesis is rejected.

(d) Type I Error.

(e) Type II Error.

Step by step solution

01

Step 1. Given Information.

The Null Hypothesis is,

H0:μ=23.

The Alternative Hypothesis is,

H0:μ≠23.

02

Part (a). Type I error.

This is the error committed to rejecting a null hypothesis H0when it is true.

The conclusion is that the mean location period of grey seals differs from 23days but in reality, the mean location period of grey seals does not differ from23days.

03

Part (b). Type II error.

This is the error committed to accepting a null hypothesis H0when it is false.

The conclusion is that the mean location period of grey seals does not differ from 23days but in reality, the mean location period of grey seals differs from 23days.

04

Part (c). Correct Decision.

The following are the two ways of making the correct decision:

  1. If H0is true, then do not reject H0.
  2. If H0is false, then reject H0.

If the mean location period of grey seals does not differs from 23days, μ=23days, then the null hypothesis is not rejected.

If the mean location period of grey seals differs from23days,μ≠23days, then the null hypothesis is rejected.

05

Part (d). Equals 23 days.

In this situation, a Type I error is committed.

The null hypothesis is not rejected because the mean location period of grey seals equals to 23days since the mean location period of grey seals equals to 23days.

06

Part (e). Differs 23 days.

In this situation, a Type II error is committed.

The null hypothesis is rejected because the mean location period of grey seals is not equals to 23days since the mean location period of grey seals differs from23 days.

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Most popular questions from this chapter

In each of Exercises 9.41-9.46 ,determine the critical values for a one-mean z-test. For each exercise, draw a graph that illustrates your answer

A left-tailed test withα=0.05

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(b) Type II error.

(c) Correct decision.

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Fair Market Rent. According to the document Out of Reach published by the National Low Income Housing Coalition, the fai market rent (FMR) for a two-bedroom unit in the United States is 949 A sample of 100 randomly selected two-bedroom units yielded the data on monthly rents, in dollars, given on the WeissStats site. Use the technology of your choice to do the following.

a. At the 5 % significance level, do the data provide sufficient evidence to conclude that the mean monthly rent for two-bedroom units is greater than the FMR of $949? Apply the one-mean t-test.

b. Remove the outlier from the data and repeat the hypothesis test in part (a).

c. Comment on the effect that removing the outlier has on the hypothesis test.

d. State your conclusion regarding the hypothesis test and explain your answer.

As we mentioned on page 378, the following relationship holds between hypothesis test and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis role="math" localid="1653038937481" H0:μ=μ0will be rejected in favor of the alternative hypothesis Ha:μ≠μ0if and only if μ0lies outside the 1-α-level confidence interval for μ. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean z-interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.

Part (a): Exercise 9.84

Part (b): Exercise9.87

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