Hypothesis Testing with Proportions

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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.B.5

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. A claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the null hypothesis.

• H_o: p <.5, where p is the true proportion of Americans who can name one justice currently serving.

• H_o:p >.5 where p is the true proportion of Americans who can name one justice currently serving.

• H_o:p =.5 where p is the true proportion of Americans who can name one justice currently serving.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. A claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the alternative hypothesis.

• H_a: p=.5, where p is the true proportion of Americans who can name one justice currently serving.

• H_a: p>.5, where p is the true proportion of Americans who can name one justice currently serving.

• H_a: p<.5, where p is the true proportion of Americans who can name one justice currently serving.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A large-scale study found that 42% of Americans play video games. A random sample of 1100 teenagers were asked whether they play games online; 575 said they did. Is there sufficient evidence to suggest that the proportion of teens who play video games is different from the national figure? Use a 5% level of significance.

Which is the correct conclusion for this test?

• Since p-value = 5.08 x 10 ^-12 < 0.05, I reject H0. There is enough evidence to suggest a difference.

• Since p-value = 5.08 x 10 ^-12 < 0.05, I fail to reject H0. There is enough evidence to suggest a difference.

• Since p-value = 5.08 > 0.05, I fail to reject H0. There is not enough evidence to suggest a difference.

• Since p-value = 5.08 > 0.05, I reject H0. There is enough evidence to suggest a difference.

A nationwide survey of 1500 adults asked about attitudes toward “alternative medicine” such as acupuncture, massage therapy, etc. Among the 1500 respondents, 660 said they would use alternative medicine if traditional medicine was not producing the results they wanted. Do these data provide enough evidence to suggest that less than half of all adults would use alternative medicine if traditional medicine didn’t produce their desired results? Use a 5% level of significance.

Which is the correct conclusion for this test?

• Since p-value = 0.001 < 0.05, I reject H0. There is enough evidence to suggest that the proportion is less than half.

• Since p-value = 0.001 > 0.05, I reject H0. There is enough evidence to suggest that the proportion is less than half.

• Since p-value = 0.001 < 0.05, I fail to reject H0. There is enough evidence to suggest that the proportion is less than half.

• Since p-value = 0.001 < 0.05, I fail to reject H0. There is not enough evidence to suggest that the proportion is less than half.

Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01.

Which is the correct conclusion for this test?

• Since p-value = 0.319 < 0.01, I reject H0. There is enough evidence to suggest a difference.

• Since p-value = 0.319 > 0.01, I reject H0. There is enough evidence to suggest a difference.

• Since p-value = 0.319 > 0.01, I fail to reject H0. There is not enough evidence to suggest a difference.

• Since p-value = 0.319 < 0.01, I fail to reject H0. There is enough evidence to suggest a difference.

A potato chip producer and a supplier of potatoes agree that each shipment must meet certain quality standards. If the producer is convinced that more than 8% of the potatoes in the shipment have blemishes, the truck will be sent away and another one would have to be sent. In a recent shipment, a SRS of 80 potatoes was selected and 7 had blemishes. Does this sample provide sufficient evidence that the criteria hasn’t been met and the shipment should be returned? Use α = 0.01.

Which is the correct conclusion for this test?

• Since p-value = .395 > .01, I reject H₀. There is not sufficient evidence to suggest that the shipment should be returned.

• Since p-value = .395 > .01, I reject H₀. There is sufficient evidence to suggest that the shipment should be returned.

• Since p-value = .395 < .01, I fail to reject H₀. There is sufficient evidence to suggest that the shipment should be returned.

• Since p-value = .395 > .01, I fail to reject H₀. There is sufficient evidence to suggest that the shipment should be returned.