1.In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525

Question

1.In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. PPIC researchers find that 68 out of 200 Central Valley residents approve of the California Legislature and that 156 out of 300 Bay Area residents approve of the California Legislature. PPIC is interested in the difference between the proportion of Central Valley and Bay Area residents who approve of the California Legislature. PPIC researchers calculate that the standard error for the proportion of Central Valley residents who approve of the California Legislature minus Bay Area residents who approve of the California Legislature is about 0.044.

Find the 95% confidence interval to estimate the difference between the proportion of Central Valley and Bay Area residents who approve of the California Legislature.

A.(-0.224, -0.136)

B.(0.094, 0.266)

C.(-0.266, -0.094)

D.(0.136, 0.224)

2. The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.04. What is the 95% confidence interval?

A.(-0.01, 0.15)

B.(0.03, 0.11)

C.(0.063, 0.077)

3.Gardeners on the west coast of the United States are investigating the difference in survival rates of two flowering plants in drought climates. Plant A has a survival rate of 0.67 and plant B has a survival rate of 0.48. The standard error of the difference in proportions is 0.097. Which of the following is the margin of error for a 99% confidence interval?

A.0.097

B.0.160

C.0.190

D.0.250

4. Students at a college in California conduct interviews to measure the proportion of scientists who are women and the proportion of teachers who are women. The scientists and teachers are randomly selected. Students find that out of 244 scientists interviewed, 71 are women. Of the 11 teachers interviewed, 9 are women.

Are the students able to use this data to test a claim about the difference in proportion of women working as scientists and the proportion of women working as teachers?

A.Yes, because subjects are randomly selected for interviews.

B.No, the students did not interview an equal number of scientists and teachers.

C.Yes, the percentages of scientists and teachers are large enough to see a difference.

D.No, the conditions for use of a normal model for the sampling distribution of sample differences is not met.

Explanation / Answer

1)

here difference in proportion=(68/200)-(156/300)=-0.18

for 95% CI ; critical value of z =1.96

hence  95% confidence interval =sample difference in proportion-/+z*std error=-0.18-/+1.96*0.04

=-0.266 ;-0.094

option C is correct

2)

95% confidence interval =0.07-/+1.96*0.04 =-0.01 ;0.15

option A is correct

3)

for 99% CI ; critical z =2.58

hence margin of error =2.58*0.097=0.25

option D

4)

D.No, the conditions for use of a normal model for the sampling distribution of sample differences is not met.

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