Hypothesis Testing for Small Samples and Proportions

You do not need BOTH null and alternate hypotheses when testing

• True

• False

The manager of a sporting goods store offered a bonus commission to his salespeople when they sold more goods. A new manager dropped the bonus system. For a random sample of six sales people, the weekly sales (in thousands of dollars) are shown in the following table with and without the bonus system
Salesperson   1 2 3 4 5 6
with bonus 2.9 3.0 5.8 4.4 5.3 5.6
w/o bonus 2.8 2.5 5.9 3.5 4.6 4.6
difference 0.1 0.5 -0.1 0.9 0.7 1.0

• Matched-Pairs T Test for a Mean

• One-Sample T Test for a Mean

• Two-Sample T Test for the Difference in Means

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S.adults who strongly agree with the given statement has dropped?

• Two-Sample Z Test for the Difference in Proportions

• Two-Sample T Test for the Difference in Means

• Matched Pairs T Test for a Mean

• One-Sample T Test for a Mean

To test a claim made about a difference of means from two samples.

Standard deviation of the populations unknown.

• 2 Sample Z-Test

• 2 Sample T-Test

• Paired T-Test

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.

Match the following

• 469

• p₀

• 5%

• α

• 7

• p̂

• 1.5%

• x

• 3%

• n

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

• p

• 0.05

• n

• 500

• α

• 0.330

• p̂

• 0.304

• x

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?

• 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

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

• 0.6

• α

• 0.58

• n

• 0.05

• x

• 58

• p

• 100

• p̂

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