Exam 14: Confidence Intervals for Means

The principal randomly selected six students to take an aptitude test.Their scores were: 71.6 81.0 88.9 80.4 78.1 72.0 Determine a 90% confidence interval for the mean score for all students.

$n = 10 , \bar { x } = 13.0 , s = 4.5$ . Find a $95 \%$ confidence interval for the mean.

Which is true about a 95% confidence interval based on a given sample? I.The interval contains 95% of the population. II.Results from 95% of all samples will lie in the interval. III.The interval is narrower than a 98% confidence interval would be.

A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test.Their mean score is 76.2 and their standarddeviation is 21.4.Construct the 95% confidence interval for the mean score of all such subjects.

Based on a sample of size 49 , a $95 \%$ confidence interval for the mean score of all students, $\mu$ , on an aptitude test is from $59.2$ to $64.8$ . Find the margin of error.

$n = 12 , \bar { x } = 28.0 , s = 5.7$ . Find a $99 \%$ confidence interval for the mean.

A certain population is bimodal.We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? I.The distribution of our sample data will be more clearly bimodal. II.The sampling distribution of the sample means will be approximately normal. III.The variability of the sample means will be smaller.

Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees of freedom: 90% confidence interval with df = 4.

Use the $t$ -tables, software, or a calculator to estimate the indicated $P$ -value: $P$ -value for $t \leq 1.76$ with 24 degrees of freedom

Analysis of a random sample of 250 Illinois nurses produced a $95 \%$ confidence interval for the mean annual salary of $\$ 42,846 < \mu$ (Nurse Salary) $< \$ 49,686$

Based on a sample of 30 randomly selected years, a 90% confidence interval for the meanannual precipitation in one city is from 48.7 inches to 51.3 inches.Find the margin of error.

Use the t-tables, software, or a calculator to estimate the indicated P-value: P-value for $\mathrm { t } \geq$ $1.76$ with 24 degrees of freedom.

A certain population is strongly skewed to the right.We want to estimate its mean, so we will collect a sample.Which should be true if we use a large sample rather than a small one? I.The distribution of our sample data will be closer to normal. II.The sampling model of the sample means will be closer to normal. III.The variability of the sample means will be greater.

Data collected by child development scientists produced the following $90 \%$ confidence interval for the average age (in months) at which children say their first word: $10.6 < \mu ($ age $) < 13.7$ .

Thirty randomly selected students took the calculus final.If the sample mean was 95 and the standard deviation was 6.4, construct a 99% confidence interval for the mean score of all students.

The amounts (in ounces) of juice in eight randomly selected juice bottles are: $15.0\quad15 .9\quad15 .8\quad15 .7\quad15 .4\quad15 .2\quad15 .2\quad15 .3$ Construct a 98% confidence interval for the mean amount of juice in all such bottles.

A credit union took a random sample of 40 accounts and yielded the following $90 \%$ confidence interval for the mean checking account balance at the institution: $\$ 2183 < \mu$ (balance) $< \$ 3828$ .

A random sample of clients at a weight loss center were given a dietary supplement to see if it would promote weight loss.The center reported that the 100 clients lost an average of 48 pounds, and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±7 pounds.

Using the t-tables, software, or a calculator, estimate the critical value of t for the given Confidence interval and degrees of freedom: 80% confidence interval with df = 11