Chap 10 learnsmart

Suppose you are performing a hypothesis test with σ unknown, n=29, and the following hypotheses: H0: μ ≤ 100 H1: μ >100 If the test statistic was 1.992, what would the p-value be?

Between 0.05 and 0.10.

Which of the following are true regarding estimation and hypothesis testing?

Both are statistical interference techniques

Which one of the following is true about the p-value?

For a two-tailed test, the P value is the area in both tails.

Which of the following statements of a test hypothesis violates the protocol for choosing null and alternative hypotheses? Select all that apply.

H0: μ > 32 H1: μ ≤ 30

Suppose you are performing a hypothesis test with σ unknown, n=23, α=0.10, and the following hypotheses: H0: μ ≥ 24 H1: μ < 24 What is the decision rule?

Reject H0 if the test statistic is less than -1.321.

A model of car claims mileage of 24 mpg. with σ = 4 mpg. A sample of 4 cars got an average of 20.5 mpg. Test H0: μ = 24 H1:C ≠ 24 at the 10% significance level.

Reject the null hypothesis

Which of the following is true about the p-value?

The closer the p-value is to 0 the more evidence to reject the null.

What is the meaning of 'level of significance' in the context of hypothesis testing?

The probability of rejecting the null hypothesis when it is true.

Choose the statement that best explains the use of the sample standard deviation in tests of the mean where the population standard deviation is not know.

The sample standard deviation is used as an estimate for the population standard deviation.

A soda bottling company fills bottles with 12 ounces of soda. Overfilling causes the company to give away free soda. Underfilling causes the company to cheat the customer. To test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: Ho: μ=12 H1: μ≠12 If we fail to reject the null, what would the interpretation be?

There is insufficient evidence to conclude that the mean is different from 12.

Select all statements that correctly describe the null hypothesis.

We either reject or fail to reject it, we cannot say that we except it or that it is true. It is developed for testing purposes.

Which one of these formulas would you use to calculate the test statistic for a test of the mean with the population standard deviation unknown?

t= (x̅-μ)/ (s/ √n)

Match the level of significance to the type of research for which it is traditionally chosen.

0.05 - consumer research 0.01 - quality assurance 0.10 - political polling

Knowing the p-value allows us to asses the weight of evidence against the null hypothesis. Match the p-value to the relative strength of evidence.

0.20- Some evidence against Ho* 0.05- Strong evidence against Ho* 0.01- Very strong evidence against Ho* 0.001- Extremely strong evidence against Ho*

Calculate the test statistic z for a population mean of 5.5, a population standard deviation of 2, a sample mean of 6.7 and a sample size of 10.

1.90

Which one of the following best describes Hypothesis Testing?

A procedure based on sample evidence and probability to see if a hypothesis is a reasonable statement.

Why do many statisticians prefer to use of "fail to reject the null hypothesis" instead of "accept the null hypothesis" ? Choose all that apply.

Because hypothesis testing does not seek to prove the null Because the null is assumed true to begin with

Which of the following sets of hypotheses require the use of a one-tailed test? Select all that apply.

H0: μ ≤ -25, H1: μ > -25 H0: μ ≥ 7.5, H1: μ < 7.5 This is a one-tailed test because of the inequality

Which of the following statements are valid descriptions of the alternate hypothesis? Select all that apply.

It is written symbolically as H1. It tells what you will conclude if you reject the null hypothesis.

Suppose a hypothesis test, using α = 0.05, is being conducted with the following null hypothesis: H0: μ = 2. Which one of the following confidence intervals would lead to rejecting the null hypothesis?

A 95% confidence interval of 3 to 4.

In the context of hypothesis testing, what is a test statistic?

A value, determined from sample information, used to test the null hypothesis.

Suppose you are performing a hypothesis test with σ unknown, n=23, and the following hypotheses: Ho: μ =24 H1: μ ≠ 24 If the test statistic was 2.026, what would the p-value be?

Between 0.05 and 0.10

A soda bottling company fills bottles with 12 ounces of soda. Overfilling causes the company to give away free soda. Underfilling causes the company to cheat the customer. To test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: Ho: μ=12 H1: μ≠12 Which of the following is the result of a Type 1 error.

Concluding the population average is not 12 when it really is.

We wish to test H0: μ ≥ 30 and H1: μ < 30 at the 0.05 level of significance. Which of these statements are correct? Select all that apply.

Fail to reject H0 if z > -1.65 Reject H0 if z < -1.65

If the test statistic for a hypothesis test (H0: μ=11) is z = 1.82 and the critical value for 5% significance is zc = 1.96, what should our conclusion be?

Fail to reject the null.

A cereal manufacturer tests a sample of 50 boxes of cereal to see if the average weight per box is 14 ounces. Which of these would be a valid null hypothesis for the given scenario?

Ho: μ=14

Which of the following statements accurately describe the p-value? Select all that apply.

If we reject the null, it is the probability of making a Type I error. The null is rejected when the p-value is less than α.

Which of the following are essential elements of hypothesis testing? Select all that apply.

It uses probability theory to determine if a hypothesis is a reasonable statement. It makes use of sample data. It is based on data collected from a sample

A paint manufacturer claims that a gallon of their paint will cover at least 1200 square feet of smooth wall with σ = 80 square feet. Thirty-six gallons of paint were tested and the average square feet covered was 1175. Conduct a hypothesis test using a 5% significance level for: H0: μ ≥ 1200H1: μ < 1200

Reject the null hypothesis

What is the 'critical value' for a hypothesis test?

The dividing point between rejecting and failing to reject the null hypothesis.

When testing a mean, where the population standard deviation is known, we calculate the test statistic using the formula z= (x̅-μ)/ (σ / √n) Match the variables to their description.

z- the test statistic x̅ - the sample mean μ - the population mean σ / √n - the standard error

A one-tailed and a two-tailed test have different critical values at the same significance level. Match the critical values to the to the correct test.

z=1.96 or -1.96 H0:μ = 0, H1:μ ≠ 0, α=0.05H0:μ = 0, H1:μ ≠ 0, α=0.05 Two-tailed test z=-2.33 H0:μ≥0, H1:μ<0, α=0.01H0:μ≥0, H1:μ<0, α=0.01 one-tailed test z=2.58 or -2.58 H0:μ=0, H1:μ≠0, α=0.01H0:μ=0, H1:μ≠0, α=0.01 two-tailed test z=1.65 H0:μ≤0, H1:μ>0, α=0.05 one-tailed test