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1. A random sample of...

1. A random sample of 92 observers produced a mean X = 25.8 and a standard deviation s = 2.6.

a) Find a 95% confidence interval for 11.

b) Find the 90% confidence interval for Jl

c) Find the 99% confidence interval for Jl

Ans. The 95% confidence interval for •• is (0, 0)

Ans. The 90% confidence interval for •• is (0, 0)

ADs. The 99% confidence interval for •• is (0, 0) Round two decimal places as needed. I

2. Healthcare workers use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 48 hospital employees who were

diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.7 and s =

12.2. average number of latex gloves used per week by all health care workers with a latex allergy. Ans. 0 c. Form a 95% confidence interval for the average number of gloves used per week by all workers with a latex allergy. Ans. (0, D) (Use integers or round decimals two places

Give a practical interpretation of the interval, part (b).

a. One can be 95% confident tbat the average number of latex gloves used per week by all workers with a latex allergy is greater than the upper boundary of

the interval.

b. Once can be 95% confident that tbe average number of latex gloves used per week by all workers with a latex allergy is less than the lower boundary of the

interval.

c. Once can be 95% confident that the latex gloves cause allergies for all who use a number of glovers contained in the interval.

d. Once can be 95% confident that the average number of latex gloves used per week by all workers with a latex allergy is in the interval.

d. Give conditions required for the interval part, (b) to be valid.

a. i, The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, that is, n > 30.

b. i. The sample selected was specifically selected from the target population. it The sample size is sufficiently large, that is, n > 1000.

c. i. The sample selected was specifically selected from the target population. ii, The sample size is sufficiently large, that is n > 30.

d. i, The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, tbat is, n> 1000.

Each child in a sample of 65 low-income children were administered a language and communication exam. The sentence complexity scores had a mean of7.51 and a standard deviation

of 8.94. Complete part a thru d.

3.. Find the sample, estimate the true mean sentence complexity score of all low-income children. Ans. 0

b. Form a 90% confidence interval for the estimate, part a. The 90% confidence interval is (0, D)

C. Give a practical interpretation of tbe interval, part b.

A. We are 90% confident that the mean sentence complexity score of all low-income children is between the end points of the confidence interval

B. We are 10% confident that the mean sentence complexity score of all low-income children is outside the confidence interval

C. We are 10% confident that the mean sentence complexity score of all low-income children is between the end points of the confidence interval

D.We are 90% confident tbat the mean sentence complexity score of all low-income children is ontside tbe confidence interval

E. An interpretation cannot be determined.

4. Suppose the true mean sentence complexity score of middle-income children is known to be 15.55. Is there evidence that the true mean for low-income children differs from

15.55?

A. Yes

B. No

The random sample shown was selected from a normal distribution. 9,3,7,8,7,2. Complete part a and b.

a) Construct a 99% confidence interval for the population mean /L (0, D) Round two decimal places as needed.

b) Assume that the sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n = 25

observation. what is the effect of increasing the sample size on tbe widtb of the confidence intervals? The confidence interval is (0, 0) Round two decimal places 5. What is the effect of the sample on the width ofthe confidence interval?

a. As the sample size increases, the width increases.

b. As the sample size increases, the width decreases.

c. As the sample size increases, the width stays the same.

6. Periodically a town water department tests the drinking water of homeowners for contaminants such as lead. The lead level in water specimens collected for sample of 10 residents of the town had a mean of2.6 mg/L and a standard deviation of 19 mg/L. a. Construct a 90% confidence interval for the mean level water specimens from the town. (0,0) Round three decimal places.

a) Find a 95% confidence interval for 11.

b) Find the 90% confidence interval for Jl

c) Find the 99% confidence interval for Jl

Ans. The 95% confidence interval for •• is (0, 0)

Ans. The 90% confidence interval for •• is (0, 0)

ADs. The 99% confidence interval for •• is (0, 0) Round two decimal places as needed. I

2. Healthcare workers use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 48 hospital employees who were

diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.7 and s =

12.2. average number of latex gloves used per week by all health care workers with a latex allergy. Ans. 0 c. Form a 95% confidence interval for the average number of gloves used per week by all workers with a latex allergy. Ans. (0, D) (Use integers or round decimals two places

Give a practical interpretation of the interval, part (b).

a. One can be 95% confident tbat the average number of latex gloves used per week by all workers with a latex allergy is greater than the upper boundary of

the interval.

b. Once can be 95% confident that tbe average number of latex gloves used per week by all workers with a latex allergy is less than the lower boundary of the

interval.

c. Once can be 95% confident that the latex gloves cause allergies for all who use a number of glovers contained in the interval.

d. Once can be 95% confident that the average number of latex gloves used per week by all workers with a latex allergy is in the interval.

d. Give conditions required for the interval part, (b) to be valid.

a. i, The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, that is, n > 30.

b. i. The sample selected was specifically selected from the target population. it The sample size is sufficiently large, that is, n > 1000.

c. i. The sample selected was specifically selected from the target population. ii, The sample size is sufficiently large, that is n > 30.

d. i, The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, tbat is, n> 1000.

Each child in a sample of 65 low-income children were administered a language and communication exam. The sentence complexity scores had a mean of7.51 and a standard deviation

of 8.94. Complete part a thru d.

3.. Find the sample, estimate the true mean sentence complexity score of all low-income children. Ans. 0

b. Form a 90% confidence interval for the estimate, part a. The 90% confidence interval is (0, D)

C. Give a practical interpretation of tbe interval, part b.

A. We are 90% confident that the mean sentence complexity score of all low-income children is between the end points of the confidence interval

B. We are 10% confident that the mean sentence complexity score of all low-income children is outside the confidence interval

C. We are 10% confident that the mean sentence complexity score of all low-income children is between the end points of the confidence interval

D.We are 90% confident tbat the mean sentence complexity score of all low-income children is ontside tbe confidence interval

E. An interpretation cannot be determined.

4. Suppose the true mean sentence complexity score of middle-income children is known to be 15.55. Is there evidence that the true mean for low-income children differs from

15.55?

A. Yes

B. No

The random sample shown was selected from a normal distribution. 9,3,7,8,7,2. Complete part a and b.

a) Construct a 99% confidence interval for the population mean /L (0, D) Round two decimal places as needed.

b) Assume that the sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n = 25

observation. what is the effect of increasing the sample size on tbe widtb of the confidence intervals? The confidence interval is (0, 0) Round two decimal places 5. What is the effect of the sample on the width ofthe confidence interval?

a. As the sample size increases, the width increases.

b. As the sample size increases, the width decreases.

c. As the sample size increases, the width stays the same.

6. Periodically a town water department tests the drinking water of homeowners for contaminants such as lead. The lead level in water specimens collected for sample of 10 residents of the town had a mean of2.6 mg/L and a standard deviation of 19 mg/L. a. Construct a 90% confidence interval for the mean level water specimens from the town. (0,0) Round three decimal places.

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