Statistics Chapter 7
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.
