Significance Test: Hypothesis and P values

What is the parameter?

• p is the true proportion of elementary students who want a career helping others

• n is 128 children

• p is the mean number of children asked

• Fail to Reject the Ho

Tags

CCSS.HSS.IC.B.4

What is the null hypothesis

• H_o: p = .39

• H_o: p < .39

• H_o: p > .39

• H_o: p ≠ .39

What is the alternative hypothesis?

• H_o: p = .39

• H_o: p < .39

• H_o: p > .39

• H_o: p ≠ .39

Identify the correct null hypothesis:

Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

The mean time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let µ denote the mean time to obtain pain relief with the new product. An experiment is conducted to verify if the new product works more quickly. What are the null and alternative hypotheses for the appropriate test of significance?

• H0 : µ = 25 vs. Ha : µ ≠ 25

• H0 : µ = 25 vs. Ha : µ < 25

• H0 : µ < 25 vs. Ha : µ = 25

• H0 : µ < 25 vs. Ha : µ > 25

• H0 : µ = 25 vs. Ha : µ > 25

When performing a significance test, we're looking for convincing evidence to __________ the null hypothesis in favor of the alternative hypothesis.

• refute

• dispute

• reject

• accept

A test of H₀: µ=60 versus H_a: µ≠60. If we test the 1000 samples and found the proportion of 25/1000, can we reject the claim or not?

Select the best response.

• We can reject the claim because the chance is too low.

• We can't reject the claim because 25/1000 > 1%

• We can reject the claim because 25/1000< 1%

• We can't reject the claim because it might be luck

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year.  She wants to know if each type of food will be equally popular so she can start ordering supplies making other plans.  To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?"  Here are the data in the table provided.  The P-value for a chi-square test for goodness of fit is 0.0129.  Which is the following is the most appropriate conclusion?

• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are equally popular.
• Because 0.0129 is less than α = 0.05, reject H₀.  There is not convincing evidence that the food choices are equally popular.
• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are not equally popular.
• Because 0.0129 is less than α = 0.05, fail to reject H₀.  There is convincing evidence that the food choices are equally popular.

Identify the correct null hypothesis:

Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

A P-value indicates:

• the probability that the null hypothesis is true
• the probability that the alternative hypothesis is true
• the probability of obtaining the results (or one more extreme) if the null hypothesis is true
• probability of a Type I error