a hard drive manufactorer would like to ensure that the meantime between failure

Question

a hard drive manufactorer would like to ensure that the meantime between failures for its new hard drive is 1 million hours. a stress test is designed that can stimulate the work load at a much faster pace. the testers assume that a test lasting 10days correlates with failure times exceedig the 1-million hour mark. in stress tests of 15 hard drives they found an average of 9.5 days, with a standard deviation of 1 day. does 90% confidence level include 10 days?

find the 80% and 90% confidence interval for a survey with n=100 and p=o.45

Explanation / Answer

a hard drive manufactorer would like to ensure that the meantime between failures for its new hard drive is 1 million hours. a stress test is designed that can stimulate the work load at a much faster pace. the testers assume that a test lasting 10days correlates with failure times exceedig the 1-million hour mark. in stress tests of 15 hard drives they found an average of 9.5 days, with a standard deviation of 1 day. does 90% confidence level include 10 days?

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

1

Sample Mean

9.5

Sample Size

15

Confidence Level

90%

Intermediate Calculations

Standard Error of the Mean

0.2582

Degrees of Freedom

14

t Value

1.7613

Interval Half Width

0.4548

Confidence Interval

Interval Lower Limit

9.05

Interval Upper Limit

9.95

90% CI = (9.05, 9.95)

This 90% confidence level does not include 10 days.

find the 80% and 90% confidence interval for a survey with n=100 and p=o.45

Confidence Interval Estimate for the Proportion 80%

Data

Sample Size

100

Number of Successes

45

Confidence Level

80%

Intermediate Calculations

Sample Proportion

0.45

Z Value

1.282

Standard Error of the Proportion

0.0497

Interval Half Width

0.0638

Confidence Interval

Interval Lower Limit

0.3862

Interval Upper Limit

0.5138

80% CI =(0.3862, 0.5138)

Confidence Interval Estimate for the Proportion 90%

Data

Sample Size

100

Number of Successes

45

Confidence Level

90%

Intermediate Calculations

Sample Proportion

0.45

Z Value

1.645

Standard Error of the Proportion

0.0497

Interval Half Width

0.0818

Confidence Interval

Interval Lower Limit

0.3682

Interval Upper Limit

0.5318

90% CI =(0.3682, 0.5318)

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

1

Sample Mean

9.5

Sample Size

15

Confidence Level

90%

Intermediate Calculations

Standard Error of the Mean

0.2582

Degrees of Freedom

14

t Value

1.7613

Interval Half Width

0.4548

Confidence Interval

Interval Lower Limit

9.05

Interval Upper Limit

9.95

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