Basic Hypothesis Testing 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

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 level of significance of 5% means:

• There's a 5% chance we're wrong

• There's a 5% chance we'll be wrong if we fail to reject the null hypothesis

• There's a 5% chance we'll be wrong if we reject the null hypothesis.

• There's a 5% chance you'll get an A on the test.

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

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 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.

• 152

• n

• 0.330

• x

• 0.05

• p

• 0.304

• p̂

• 500

• α

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

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

• 0.58

• α

• 0.6

• p̂

• 100

• x

• 0.05

• p

• 58

• n

Use the notation to state the alternative hypothesis and null hypothesis: "Less than 4% of high school students take Statistics."

• H_o : X ≥ 4% and H₁ : X > 4%

• H_o : X ≤ 4% and H₁ : X < 4%

• H_o : X ≥ 4% and H₁ : X < 4%

• H_o : X > 4% and H₁ : X ≤ 4%