EBK INTRODUCTION TO THE PRACTICE OF STA
EBK INTRODUCTION TO THE PRACTICE OF STA
8th Edition
ISBN: 9781319116828
Author: Moore
Publisher: VST
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Chapter 8, Problem 101E

(a)

To determine

To find: The 95% confidence interval for question (a).

(a)

Expert Solution
Check Mark

Answer to Problem 101E

Solution: The 95% confidence interval for question (a) is (0.5278,0.5822).

Explanation of Solution

Calculation: The formula for confidence interval is defined as;

p^±m

Where m is the margin of error which is defined as:

m=z*×SEp^

z* is the value of the standard normal density curve and SEp^ is the standard error . The standard error is the estimate of the standard deviation of a statistic. The formula for standard error SEp^ of sample proportion p^ and sample size n is defined as:

SEp^=p^(1p^)n

The sample proportion is provided as p^=0.555 and the sample size is n=1280 . Substitute the values in the standard error formula. So,

SEp^=0.555(10.555)1280=0.2469751280=0.0139

The value of z* for 95% confidence level is z*=1.96 from the standard normal table.

So, the margin of error is obtained as:

m=z*×SEp^=1.96×0.0139=0.027244

The 95% confidence interval for question (a) is obtained as;

0.555±0.027244=(0.5550.027244,0.555+0.027244)=(0.5278,0.5822)

Interpretation: There is 95% confidence that between 52.78% and 58.22% of students feel burdened by their student loan payments.

(b)

To determine

To find: The 95% confidence interval for question (b).

(b)

Expert Solution
Check Mark

Answer to Problem 101E

Solution: The 95% confidence interval for question (b) is (0.5168,0.5712).

Explanation of Solution

Calculation: The formula for confidence interval is defined as;

p^±m

Where m is the margin of error which is defined as:

m=z*×SEp^

z* is the value of the standard normal density curve and SEp^ is the standard error . The standard error is the estimate of the standard deviation of a statistic. The formula for standard error SEp^ of sample proportion p^ and sample size n is defined as:

SEp^=p^(1p^)n

The sample proportion is provided as p^=0.544 and the sample size is n=1280 . Substitute the values in the standard error formula. So,

SEp^=0.544(10.544)1280=0.2480641280=0.0139

The value of z* for 95% confidence level is z*=1.96 from the standard normal table.

So, the margin of error is obtained as:

m=z*×SEp^=1.96×0.0139=0.027244

The 95% confidence interval for question (b) is obtained as;

0.544±0.027244=(0.5440.027244,0.544+0.027244)=(0.5168,0.5712)

Interpretation: There is 95% confidence that between 51.68% and 57.12% of students would like to borrow lesser loan if the loan begins again.

(c)

To determine

To find: The 95% confidence interval for question (c).

(c)

Expert Solution
Check Mark

Answer to Problem 101E

Solution: The 95% confidence interval for question (c) is (0.3169,0.3691).

Explanation of Solution

Calculation: The formula for confidence interval is defined as;

p^±m

Where m is the margin of error which is defined as:

m=z*×SEp^

z* is the value of the standard normal density curve and SEp^ is the standard error . The standard error is the estimate of the standard deviation of a statistic. The formula for standard error SEp^ of sample proportion p^ and sample size n is defined as:

SEp^=p^(1p^)n

The sample proportion is provided as p^=0.343 and the sample size is n=1280 . Substitute the values in the standard error formula. So,

SEp^=0.343(10.343)1280=0.2253511280=0.0133

The value of z* for 95% confidence level is z*=1.96 from the standard normal table.

So, the margin of error is obtained as:

m=z*×SEp^=1.96×0.0133=0.026068

The 95% confidence interval for question (b) is obtained as;

0.343±0.026068=(0.3430.026068,0.343+0.026068)=(0.3169,0.3691)

Interpretation: There is 95% confidence that between 31.69% and 36.19% of students disagreed that the education loans are not more financial hardship than expected at the time of taking loans.

(d)

To determine

To find: The 95% confidence interval for question (d).

(d)

Expert Solution
Check Mark

Answer to Problem 101E

Solution: The 95% confidence interval for question (d) is (0.5620,0.6160).

Explanation of Solution

Calculation: The formula for confidence interval is defined as;

p^±m

Where m is the margin of error which is defined as:

m=z*×SEp^

z* is the value of the standard normal density curve and SEp^ is the standard error . The standard error is the estimate of the standard deviation of a statistic. The formula for standard error SEp^ of sample proportion p^ and sample size n is defined as:

SEp^=p^(1p^)n

The sample proportion is provided as p^=0.589 and the sample size is n=1280 . Substitute the values in the standard error formula. So,

SEp^=0.589(10.589)1280=0.2420791280=0.0138

The value of z* for 95% confidence level is z*=1.96 from the standard normal table.

So, the margin of error is obtained as:

m=z*×SEp^=1.96×0.0138=0.027048

The 95% confidence interval for question (b) is obtained as;

0.589±0.027048=(0.5890.027048,0.589+0.027048)=(0.5620,0.6160)

Interpretation: There is 95% confidence that between 56.20% and 61.60% of students agreed that payment of loans is unpleasant even though the benefits of education loans are worthy.

(e)

To determine

To find: The 95% confidence interval for question (e).

(e)

Expert Solution
Check Mark

Answer to Problem 101E

Solution: The 95% confidence interval for question (e) is (0.5620,0.6160).

Explanation of Solution

Calculation: The formula for confidence interval is defined as;

p^±m

Where m is the margin of error which is defined as:

m=z*×SEp^

z* is the value of the standard normal density curve and SEp^ is the standard error . The standard error is the estimate of the standard deviation of a statistic. The formula for standard error SEp^ of sample proportion p^ and sample size n is defined as:

SEp^=p^(1p^)n

The sample proportion is provided as p^=0.589 and the sample size is n=1280 . Substitute the values in the standard error formula. So,

SEp^=0.589(10.589)1280=0.2420791280=0.0138

The value of z* for 95% confidence level is z*=1.96 from the standard normal table.

So, the margin of error is obtained as:

m=z*×SEp^=1.96×0.0138=0.027048

The 95% confidence interval for question (b) is obtained as;

0.589±0.027048=(0.5890.027048,0.589+0.027048)=(0.5620,0.6160)

Interpretation: There is 95% confidence that between 56.20% and 61.60% of students are satisfied with the investment for education loan which worth for career opportunities.

(f)

To determine

To find: The 95% confidence interval for question (f).

(f)

Expert Solution
Check Mark

Answer to Problem 101E

Solution: The 95% confidence interval for question (f) is (0.6903,0.7397).

Explanation of Solution

Calculation: The formula for confidence interval is defined as;

p^±m

Where m is the margin of error which is defined as:

m=z*×SEp^

z* is the value of the standard normal density curve and SEp^ is the standard error . The standard error is the estimate of the standard deviation of a statistic. The formula for standard error SEp^ of sample proportion p^ and sample size n is defined as:

SEp^=p^(1p^)n

The sample proportion is provided as p^=0.715 and the sample size is n=1280 . Substitute the values in the standard error formula. So,

SEp^=0.715(10.715)1280=0.2037751280=0.0126

The value of z* for 95% confidence level is z*=1.96 from the standard normal table.

So, the margin of error is obtained as:

m=z*×SEp^=1.96×0.0126=0.024696

The 95% confidence interval for question (b) is obtained as;

0.715±0.024696=(0.7150.024696,0.715+0.024696)=(0.6903,0.7397)

Interpretation: There is 95% confidence that between 69.03% and 73.97% of students are satisfied with the investment for student loan which worth for personal growth.

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Chapter 8 Solutions

EBK INTRODUCTION TO THE PRACTICE OF STA

Ch. 8.1 - Prob. 11UYKCh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 38ECh. 8.2 - Prob. 45UYKCh. 8.2 - Prob. 46UYKCh. 8.2 - Prob. 47UYKCh. 8.2 - Prob. 48UYKCh. 8.2 - Prob. 49UYKCh. 8.2 - Prob. 50UYKCh. 8.2 - Prob. 51UYKCh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Prob. 63ECh. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 69ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 70ECh. 8.2 - Prob. 71ECh. 8 - Prob. 72ECh. 8 - Prob. 73ECh. 8 - Prob. 74ECh. 8 - Prob. 75ECh. 8 - Prob. 76ECh. 8 - Prob. 77ECh. 8 - Prob. 94ECh. 8 - Prob. 79ECh. 8 - Prob. 80ECh. 8 - Prob. 81ECh. 8 - Prob. 82ECh. 8 - Prob. 83ECh. 8 - Prob. 84ECh. 8 - Prob. 85ECh. 8 - Prob. 86ECh. 8 - Prob. 87ECh. 8 - Prob. 88ECh. 8 - Prob. 89ECh. 8 - Prob. 90ECh. 8 - Prob. 95ECh. 8 - Prob. 96ECh. 8 - Prob. 97ECh. 8 - Prob. 98ECh. 8 - Prob. 99ECh. 8 - Prob. 92ECh. 8 - Prob. 93ECh. 8 - Prob. 78ECh. 8 - Prob. 100ECh. 8 - Prob. 101E
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