AP Stats - 10.1 Differences in Proportions Summary Questions

A sample survey interviews SRSs of 500 female college students and 550 male college students. Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer. In all, 410 of the females and 484 of the males say they worked for pay last summer.

Take $p_m$ and $p_f$  to be the proportions of all college males and females who worked last summer. The hypotheses to be tested are 

•  $H_o:\ p_m-p_f=0$  versus $H_a:\ p_m-p_f\ne0$  

•  $H_o:\ p_m-p_f=0$  versus $H_a:\ p_m-p_f>0$  

•  $H_o:\ p_m-p_f=0$  versus $H_a:\ p_m-p_f<0$  

•  $H_o:\ p_m-p_f>0$  versus $H_a:\ p_m-p_f=0$  

•  $H_o:\ p_m-p_f\ne0$  versus $H_a:\ p_m-p_f=0$  

A sample survey interviews SRSs of 500 female college students and 550 male college students. Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer. In all, 410 of the females and 484 of the males say they worked for pay last summer.

The researchers report that the results were statistically significant at the 1% level. Which of the following is the most appropriate conclusion?

• Because the P-value is less than 1%, fail to reject $H_o$ . There is not convincing evidence that the proportion of male college students in the study who worked for pay last summer is different from the proportion of female college students in the study who worked for pay last summer.

• Because the P-value is less than 1%, fail to reject $H_o$ . There is not convincing evidence that the proportion of all male college students who worked for pay last summer is different from the proportion of all female college students who worked for pay last summer.

• Because the P-value is less than 1%, reject $H_o$ . There is convincing evidence that the proportion of all male college students who worked for pay last summer is the same as the proportion of all female college students who worked for pay last summer.

• Because the P-value is less than 1%, reject $H_o$ . There is convincing evidence that the proportion of all male college students in the study who worked for pay last summer is different from the proportion of all female college students in the study who worked for pay last summer.

• Because the P-value is less than 1%, reject $H_o$ . There is convincing evidence that the proportion of all male college students who worked for pay last summer is different from the proportion of all female college students who worked for pay last summer.

Tags

CCSS.HSS.IC.B.4

A sample survey interviews SRSs of 500 female college students and 550 male college students. Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer. In all, 410 of the females and 484 of the males say they worked for pay last summer.

Which of the following is the correct margin of error

for a 99% confidence interval for the difference in

the proportion of male and female college students

who worked for pay last summer?

• $2.567\sqrt{\frac{0.851\left(0.149\right)}{550}+\frac{0.851\left(0.149\right)}{500}}$

• $2.567\sqrt{\frac{0.851\left(0.149\right)}{1050}}$

• $2.567\sqrt{\frac{0.880\left(0.120\right)}{550}+\frac{0.820\left(0.180\right)}{500}}$

• $1.960\sqrt{\frac{0.851\left(0.149\right)}{550}+\frac{0.851\left(0.149\right)}{500}}$

• $1.960\sqrt{\frac{0.880\left(0.120\right)}{550}+\frac{0.820\left(0.180\right)}{500}}$

Tags

CCSS.HSS.IC.B.4

In an experiment to learn whether Substance M can help restore memory, the brains of 20 rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, 10 rats (determined at random) were given M and 7 of them succeeded in the maze. Only 2 of the 10 control rats were successful. The two-sample z test for “no difference” against “a significantly higher proportion of

the M group succeeds”

• gives z = 2.25, P < 0.02

• gives z = 2.60, P < 0.005

• gives z = 2.25, P < 0.04 but not < 0.02

• should not be used because the Random condition is violated

• should not be used because the Large Counts condition is violated

(CI - Inf3) In general, how does doubling the sample size change the confidence interval size?

• Doubles the interval size

• Halves the interval size

• Multiplies the interval size by 1.414

• Divides the interval size by 1.414

• This question cannot be answered without knowing the sample size.

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CCSS.HSS.IC.B.4

(HT - Inf8) A survey of 1,000 Americans reveals that 525 believe that whales are an endangered animal and should have protection from the fishing industry. In a survey of 750 Japanese, 325 believe that whales are an endangered animal and should have protection from the fishing industry. To test at the 5 percent significance level whether or not the data are significant evidence that the proportion of Japanese who believe whales need protection is less than the proportion of Americans with this belief, a student sets up the following:

Ho: p = .525
Ha: p < .525

where p is the proportion of Japanese who believe that whales need protection. Which of the following is a true statement?

• The student has set up a correct hypothesis test.

• Given the large sample sizes, a 1 percent significance level would be more appropriate.

• A two-sided test would be more appropriate.

• Given that $\frac{525+325}{1000+750}=.486$ ,  $H_a:\ p\ <\ .486$  would be more appropriate

• A two-population difference in proportions hypothesis test would be more appropriate

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CCSS.HSS.IC.B.4

(HT - Inf14) Which of the following are true statements?

I. Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

II. A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.

III. The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

• I and II

• I and III

• II and III

• I, II, and III

• None of the above gives the complete set of true responses

(CI - Inf 21) Should there be more restrictions on handguns? In a pre-Columbine survey, 255 out of 1,020 adults answered in the affirmative; in a 2000 post-Columbine survey, 352 out of 1,100 answered affirmatively. Establish a 90 percent confidence interval estimate of the difference between the proportions of adults in 1995 and 2000 who support more restrictions on handguns.

• $\left(.25-.32\right)\pm1.645\sqrt{\frac{\left(.25\right)\left(.75\right)}{1,020}+\frac{\left(.32\right)\left(.68\right)}{1,100}}$

• $\left(.25-.32\right)\pm1.645\sqrt{\frac{\left(.25\right)\left(.75\right)}{\sqrt{1,020}}+\frac{\left(.32\right)\left(.68\right)}{\sqrt{1,100}}}$

• $\left(.25-.32\right)\pm1.96\sqrt{\frac{\left(.25\right)\left(.75\right)}{1,020}+\frac{\left(.32\right)\left(.68\right)}{1,100}}$

• $\left(.25-.32\right)\pm1.96\sqrt{\frac{\left(.25\right)\left(.75\right)}{\sqrt{1,020}}+\frac{\left(.32\right)\left(.68\right)}{\sqrt{1,100}}}$

• $\left(.25-.32\right)\pm2.576\left(\frac{\sqrt{\left(.25\right)\left(.75\right)}}{1,020}+\frac{\sqrt{\left(.32\right)\left(.68\right)}}{1,100}\right)$

Tags

CCSS.HSS.IC.B.4