Proportion Hypothesis Testing

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

What is the critical value (in a test about proportions) for a left-tailed test with α = 0.05 and n ≥ 30. 

• z₀ = -1.645

• z₀ = -2.33

• z₀ = -1.96

• z₀ = 2.58

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

A large school district was considering changing the start times to its schools. The change would involve high schools starting later and elementary schools starting earlier. The school district was curious if parents supported this change, so they surveyed separate random samples of parents from both types of school in the district.

The school district wants to determine if the proportion of parents who support the change is significantly different for each type of school. Assume that all conditions have been met.

Which of the following would be an appropriate test statistic for the district's test?

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Caroline thinks she can flip a coin so it lands showing heads more often with her right hand. She flipped a coin 40 times with each hand. She wants to test whether she gets more heads with her right hand than her left hand. (Assume all conditions have been met.)

Which of the following would be an appropriate test statistic for their test?

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The manufacturer of soft drink A advertises that they have 60% of the soft drink market. A consumer group that monitors sales thinks that this percentage is no longer true. In a blind taste test of 100 people, 58 people selected soft drink A.  Is this evidence that the percentage of the market for soft drink A is different than advertised? Match the following

• 0.05

• α

• 100

• p̂

• 58

• x

• 0.58

• p

• 0.6

• n

The manufacturer of soft drink A advertises that they have 60% of the soft drink market. A consumer group that monitors sales thinks that this percentage is no longer true. In a blind taste test of 100 people, 58 people selected soft drink A. Is this evidence that the percentage of the market for soft drink A is different than advertised?

• p = 0.6

• p ≠ 0.6

• p0 = 0.6

• p0 < 0.6

• p>0.6

• p = 0.58

• p≠0.58

• p0 = 0.58

• p0 ≠ 0.58

A political consultant wondered if support for a candidate was significantly different between men and women. The consultant surveyed a random sample of voters.

The consultant wants to test if these results suggest a significant difference in support between men and women. Assume that all conditions have been met.

Which of the following would be an appropriate test statistic for their test?

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A leading research firm reports that 33% of young adults have completed a college degree.  One state leader who is trying to create more scholarship money for college believes that the rate is lower than that in his state.  The state leader commissions a study that surveys 500 young adults in the same age bracket as the national study to see if they have completed a college degree.  Of the 500 interviewed, 152 have completed a college degree.  Conduct a hypothesis test to see if the state leader has evidence to support his claim.

p-value = ​ (a)   ​ (b)   0.05

We ​ (c)   the ​ (d)   hypothesis.

There ​ (e)   enough evidence to support the claim that the rate is lower than that in his state.

• 0.1082

• fail to reject

• is not

• >

• null

• alternative

• <

• 0.0158

• reject

• is

In one year, a national vital statistics report indicated that about 3% of all births produced twins.  Data from a large city hospital found only 7 sets of twins were born to 469 teenage girls.  Does that suggest that mothers under age 20 may be less likely to have twins?  Test at a .05 significance level. Identify the hypothesis statement: H₀ : ​ (a)   H_a : ​ (b)  

• p = 0.03

• p < 0.03

• µ= 0.03

• μ< 0.03

• p0=0.03

• p0<0.03

• p>0.03

• p = 0.05

• μ = 0.05