Homework on Confidence Intervals, Hypothesis Testing and Proportions

This statistics homework assignment provides solutions to a range of problems related to confidence intervals and hypothesis testing. The problems cover topics such as finding critical values for different confidence levels, calculating the margin of error, constructing confidence intervals for population proportions, and conducting hypothesis tests using p-values. Specific questions address scenarios involving sample sizes, sample proportions, and test statistics. The solutions demonstrate the application of statistical concepts to real-world problems, offering detailed step-by-step calculations and explanations. This document is contributed by a student and is available on Desklib, a platform offering a variety of study tools and resources.

CHAPTER 8 HOMEWORK
QUESTION 1
You intend to estimate a population mean with a confidence interval. You believe the population
to have a normal distribution. Your sample size is 14.
Find the critical value that corresponds to a confidence level of 85%.
(Report answer accurate to three decimal places with appropriate rounding.)
tα/2 = ±1.530
QUESTION 2…
If n=120 and ˆp^ (p-hat) =0.75, find the margin of error at a 95% confidence level
Give your answer to three decimals
Margin of error = 0.078
QUESTION 3…
Out of 500 people sampled, 365 had kids. Based on this, construct a 99% confidence interval for
the true population proportion of people with kids.
Give your answers as decimals, to three places
< p <
QUESTION 4…
Assume that a sample is used to estimate a population proportion p. Find the 99% confidence
interval for a sample of size 291 with 160 successes. Enter your answer as a tri-linear inequality
using decimals (not percents) accurate to three decimal places.
< p <
Answer should be obtained without any preliminary rounding. However, the critical value may
be rounded to 3 decimal places.
0.679 0.781
0.475 0.625

QUESTION 5…
We wish to estimate what percent of adult residents in a certain county are parents. Out of 500
adult residents sampled, 380 had kids. Based on this, construct a 90% confidence interval for the
proportion p of adult residents who are parents in this county.
Give your answers as decimals, to three places.
< p <
QUESTION 6…
Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence
interval for a sample of size 86 with 71 successes. Enter your answer as an open-interval (i.e.,
parentheses) using decimals (not percents) accurate to three decimal places.
99.5% C.I. =
Answer should be obtained without any preliminary rounding. However, the critical value may
be rounded to 3 decimal places.
QUESTION 7…
For a confidence level of 98% with a sample size of 14, find the critical t value.
Critical value tα/2 = 2.650
QUESTION 8…
If n=27, ¯x¯(x-bar) = 41, and s=3, find the margin of error at a 95% confidence level
Give your answer to two decimal places.
QUESTION 9…
In a survey, 25 people were asked how much they spent on their child's last birthday gift. The
results were roughly bell-shaped with a mean of $38 and standard deviation of $9. Find the
margin of error at a 80% confidence level.
Give your answer to two decimal places.
0.729 0.791
(0.711, 0.940)
1.19

Margin of error = 2.37
QUESTION 10
If n=30, ¯x (x-bar) = 49, and s=10, construct a confidence interval at a 90% confidence level.
Assume the data came from a normally distributed population.
Give your answers to one decimal place.
< μ <
45.9 52.1