Assuming normality, construct the requested confidence interval. A sociologist is interested in the age at which...

Assuming normality, construct the requested confidence interval.

A sociologist is interested in the age at which a mother has her first child. A random sample of 20 recent births yielded an average maternal age to be 30 years with a standard deviation of 6.2 years.

Construct a 99% confidence interval for the mean age at which a mother has her first child.

Question 17 options:

	(27.10, 32.90)
	(26.43, 33.57)
	(27.28, 32.72)
	(27.60, 32.40)
	(26.03, 33.97)

Solutions

Expert Solution

c )solution

Given that,

= 30

s =6.2

n = 20

Degrees of freedom = df = n - 1 = 20- 1 = 19

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2 df = t0.005,19 = 2.861 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.861* ( 6.2/ $\sqrt$ 20) = 3.97

The 99% confidence interval is,

- E < < + E

30 - 3.97< <30 + 3.97

(26.03, 33.97)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Call me: A sociologist wants to construct a 98% confidence interval for the proportion of children...

Call me: A sociologist wants to construct a 98% confidence interval for the proportion of children aged 8-10 living in New York who own a cell phone. (a) A survey by the National Consumers League taken in 2012 estimated the nationwide proportion to be 0.28. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.03?

27. Call me: A sociologist wants to construct a 95% confidence interval for the proportion of...

27. Call me: A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–10 living in New York who own a cell phone. a. A survey by the National Consumers League estimated the nationwide proportion to be 0.32. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02? b. Estimate the sample size needed if no estimate of p is available. c. If the...

Use the given data to construct a confidence interval of the requested level. x = 113,...

Use the given data to construct a confidence interval of the requested level. x = 113, n = 176, confidence level 98% Group of answer choices 0.558 < p < 0.726 0.571 < p < 0.713 0.446 < p < 0.838 0.606 < p < 0.678

Use the given data to construct a confidence interval of the requested level. x = 91,...

Use the given data to construct a confidence interval of the requested level. x = 91, n = 174, confidence level 98%

A sociologist wants to construct a 90% confidence interval for the proportion of children aged 8-10...

A sociologist wants to construct a 90% confidence interval for the proportion of children aged 8-10 living in New York who own a cell phone. A survey by the National Consumers League taken in 2012 estimates the nationwide proportion to be 0.41. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?

Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the...

Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: ? (Round to four decimal places as needed.) Upper bound:? (Round to four decimal places as needed.) (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.15%? The mean rate of return for the company stock if the rate of return of the index is 3.15%...

Assuming that the population is normally distributed, construct a 90 % confidence interval for the population...

Assuming that the population is normally distributed, construct a 90 % confidence interval for the population mean, based on the following sample size of n equals 5. 1, 2, 3, 4, and 29 In the given data, replace the value 29 with 5 and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval, in general.

Assuming that the population is normally distributed, construct a 99% confidence interval for the population mean,...

Assuming that the population is normally distributed, construct a 99% confidence interval for the population mean, based on the following sample size of n=7. 1, 2, 3,4, 5, 6,and 30 Change the number 30 to 7 and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval. Find a 99 % confidence interval for the population mean. (Round to two decimal places as needed.) Change the number 30...

Assuming that the population is normally distributed, construct a 9090% confidence interval for the population mean...

Assuming that the population is normally distributed, construct a 9090% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 11 22 33 33 66 66 77 88 Full data set Sample B: 11 22 33 44 55 66 77 88 Construct a 9090% confidence interval for the population mean for sample A. nothing less than or equals≤muμless...

Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean...

Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 1 1 4 4 5 5 8 8 Sample B: 1 2 3 4 5 6 7 8 a. Construct a 90% confidence interval for the population mean for sample A b. Construct a 90% confidence interval...

Subjects