Statistics Chapter 7

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What are the two decisions that you can make from performing a hypothesis​ test?

Fail to reject the null hypothesis Reject the null hypothisis

A large​ P-value in a test will favor a rejection of the null hypothesis.

False, a small p-value supports rejecting the null hypothesis.

If you want to support a​ claim, write it as your null hypothesis.

False. If you want to support a claim, write is as your alternative hypothesis.

In a hypothesis​ test, you assume the alternative hypothesis is true.

False. In a hypothesis test, you assume the null hypothesis is true.

In hypothesis​ testing, does choosing between the critical value method or the​ P-value method affect your​ conclusion? Explain.

No, because both involve comparing the test​ statistic's probability with the level of significance

Two-tailed test

A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution.

Left​-tailed test

A one-tailed test in which the sample outcome is hypothesized to be at the left tail of the sampling distribution.

Right-tailed test

A one-tailed test in which the sample outcome is hypothesized to be at the right tail of the sampling distribution.

Describe the type I error and the type II error for a hypothesis tests of the given claim. The proportion of settled medical malpractice suits is 0.26. Which of the following is a type II​ error?

Fail to reject the claim that the proportion of settled malpractice suits is 0.26 when the proportion is actually different from 0.26.

Identify the type I error and the type II error for a hypothesis test of the indicated claim. The percentage of households with Internet access is less than 60 %. Identify the type II error

Fail to reject the null hypothesis that the percentage of households with Internet access is greater than or equal to 60 % when it is actually false.

An amusement park claims that the mean daily attendence at the park is 22,000 Choose the correct null and alternative hypotheses below.

Ho = μ = 22,000 Ha = μ ≠ 22,000

A company claims that its brands of paint have a mean drying time of more than 10 minutes. Choose the correct null and alternative hypotheses below.

Ho = μ ≤ 10 Ha = μ > 10

A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 7 hours. Choose the correct null and alternative hypotheses below.

Ho = μ ≤ 7 Ha = μ > 7

The standard deviation of the base price of a certain type of​ all-terrain vehicle is equal to ​$338. Choose the correct null and alternative hypotheses below.

Ho = σ = 338 Ha = σ ≠ 338

Explain how to decide when a normal distribution can be used to approximate a binomial distribution.

If np ≥ 5 and nq ≥ ​5, the normal distribution can be used.

Explain the difference between the​ z-test for μ using rejection​ region(s) and the​ z-test for μ using a​ P-value.

In the​ z-test using rejection​ region(s), the test statistic is compared with critical values. The​ z-test using a​ P-value compares the​ P-value with the level of significance α. A rejection region​ (or critical​ region) of the sampling distribution is the range of values for which the null hypothesis is not probable. A critical value z0 separates the rejection region from the nonrejection region. To use a rejection region to conduct a​ z-test, calculate the standardized test statistic z. If the standardized test statistic is in the rejection​ region, then reject H0. If the standardized test statistic is not in the rejection​ region, then fail to reject H0. To use a​ P-value to make a conclusion in a hypothesis​ test, compare the​ P-value with α. If P ≤ α​, then reject H0. If P > α​, then fail to reject H0.

Describe the type I error and the type II error for a hypothesis tests of the given claim. The proportion of settled medical malpractice suits is 0.26. Which of the following is a type I​ error?

Reject the claim that the proportion of settled malpractice suits is 0.26 when the proportion is actually 0.26.

Identify the type I error and the type II error for a hypothesis test of the indicated claim. The percentage of households with Internet access is less than 60 %. Identify the type I error.

Reject the null hypothesis that the percentage of households with Internet access is greater than or equal to 60 % when it is actually true.

A company claims that its brands of paint have a mean drying time of more than 10 minutes. Identify which is the claim.

The alternative hypothesis Ha = μ > 10

A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 7 hours. Identify which is the claim.

The alternative hypothesis Ha​: μ > 7 is the claim.

An amusement park claims that the mean daily attendence at the park is 22,000 Identify which is the claim.

The null hypothesis Ho = μ = 338

The standard deviation of the base price of a certain type of​ all-terrain vehicle is equal to ​$338. Identify which is the claim.

The null hypothesis Ho = σ = 338

Identify which is the claim.

The null hypothesis Upper H 0​: p=0.24 is the claim.

How are null and alternative hypothesis related?

They are complements.

Choose the correct null and alternative hypotheses below.

Upper H 0​: p = 0.24 Upper H Subscript a​: p not equals 0.24

The alternative​ hypothesis, Ha​, is the

complement of the null hypothesis

What are the two types of hypotheses used in a hypothesis​ test?

null and alternative

According to a recent​ survey, 24​% of college students own a credit card. Write the claim as a mathematical statement.

p = 0.24

A null​ hypothesis, Upper H 0​, is a

statistical hypothesis that contains a statement of equality

An amusement park claims that the mean daily attendence at the park is 22,000 Write the claim as a mathematical statement.

μ = 22,000

A company claims that its brands of paint have a mean drying time of more than 10 minutes. Write the claim as a mathematical statement.

μ > 10

A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 7 hours. Write the claim as a mathematical statement.

μ > 7

The standard deviation of the base price of a certain type of​ all-terrain vehicle is equal to ​$338. Write the claim as a mathematical statement.

σ = 338

A null hypothesis is rejected with a level of significance of 0.05. Is it also rejected with a level of significance of​ 0.10? Explain.

​Yes, the claim would be rejected because the​ P-value would be less than 0.10.


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