Question

1-

The table to the right shows the results of a survey in which 2558

adults from Country A, 1123 adults from Country B, and 1089

adults from Country C were asked if they believe climate change poses a large threat to the world. Complete parts (a), (b), and (c).

Does climate change pose a large threat to the world? Country Yes 99% CI A 27

%	(0.247 comma 0.293

)
B	55

%	(0.512 comma 0.588

)
C	28

%	(0.245 comma 0.315

)

(a) Determine whether it is reasonably possible that the proportion of adults from Country A and the proportion of adults from Country B are equal and explain your reasoning. Choose the correct answer below.

A.Yes, because the two confidence intervals overlap.

B.Yes, because the two confidence intervals do not overlap.

C.No, because the two confidence intervals do not overlap.

D.No, because the two confidence intervals overlap.

(b) Determine whether it is reasonably possible that the proportion of adults from Country B and the proportion of adults from Country C are equal and explain your reasoning. Choose the correct answer below.

A.Yes, because the two confidence intervals do not overlap.

B.No, because the two confidence intervals do not overlap.

C.Yes, because the two confidence intervals overlap.

D.No, because the two confidence intervals overlap.

(c) Determine whether it is reasonably possible that the proportion of adults from Country A and the proportion of adults from Country C are equal and explain your reasoning. Choose the correct answer below.

A.Yes, because the two confidence intervals overlap.

B.Yes, because the two confidence intervals do not overlap.

C.No, because the two confidence intervals do not overlap.

D.No, because the two confidence intervals overlap.

2- In a survey of 608 males ages 18-64, 399 say they have gone to the dentist in the past year.

Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval for the population proportion p is (.... , .....)

The 95% confidence interval for the population proportion p is (..... , .....)

Interpret your results of both confidence intervals.

A.With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.

B.With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

C.With the given confidence, it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

Which interval is wider?

A-The 90% confidence interval

B-The 95% confidence interval

Answer 1

Solution:-

Country	Yes	99% C.I
A	27	(0.247, 0.293)
B	55	(0.512, 0.588)
C	28	(0.245, 0.315)

1)

a) (C) No, because the two confidence intervals do not overlap.

b) (B) No, because the two confidence intervals do not overlap.

c) (A) Yes, because the two confidence intervals overlap.

2) The 90% confidence interval for the population proportion p is C.I = (0.6246, 0.6879).

C.I = 0.65625 + 1.645 × 0.01926

C.I = 0.65625 + 0.03169

C.I = (0.6246, 0.6879)

The 95% confidence interval for the population proportion p is C.I = ( 0.6185, 0.6939)

C.I = 0.65625 + 1.96 × 0.01926

C.I = 0.65625 + 0.03775

C.I = ( 0.6185, 0.6939)

B) With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

B) The 95% confidence interval.