Exam 9: Estimating the Value of a Parameter Using Confidence Intervals

Provide an appropriate response. -To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of $25.2$ milligrams and standard deviation of $2.7$ milligrams for a sample of $\mathrm { n } = 9$ cigarettes. The FDA claims that the mean nicotine content exceeds $28.3$ milligrams for this brand of cigarette, and their stated reliability is $95 \%$ . Do you agree?

Find Critical Values for the Chi-Square Distribution -Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$ , for $90 \%$ confidence and $\mathrm { n } = 15$ .

Choose the one alternative that best completes the statement or answers the question. -A random sample of 40 part-time workers has a mean annual earnings of $\$ 3120$ and a population standard deviation of $\$ 677$ . Compute the $95 \%$ confidence interval for $\mu$ .

Provide an appropriate response. -A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a $99 \%$ confidence interval to estimate the true proportion of students on financial aid.

Provide an appropriate response. -In a survey of 10 musicians, 2 were found to be left-handed. Is it practical to construct the $90 \%$ confidence interval for the population proportion, p? Explain.

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -As the level of confidence increases the number of item to be included in a sample will decrease when the error and the standard deviation are held constant.

Provide an appropriate response. -A local bank needs information concerning the savings account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $\$ 686.75$ with a standard deviation of $\$ 256.20$ . Find a $98 \%$ confidence interval for the true mean. Assume that the account balances are normally distributed.

Find Critical Values for the Chi-Square Distribution -Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$ , for $98 \%$ confidence and $\mathrm { n } = 20$ .

Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal with no outliers. -Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6 minutes, their pulses were measured and the following data were obtained: 105 94 98 88 104 101 99 85 84 124 122 114 97 101 90

Provide an appropriate response. -Construct a $95 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 25 randomly English majors has a mean test score of $81.5$ with a standard deviation of $10.2$ .

Provide an appropriate response. -Construct a $99 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of $22.4$ years with a standard deviation of $3.8$ years.

Provide an appropriate response. -A confidence interval was used to estimate the proportion of math majors that are female. A random sample of 72 math majors generated the following confidence interval: $( 0.438,0.642 )$ . Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within $3 \%$ using $99 \%$ reliability?

Choose the one alternative that best completes the statement or answers the question. -In a recent study of 42 eighth graders, the mean number of hours per week that they played video games was $19.6$ with a population standard deviation of $5.8$ hours. Compute the $98 \%$ confidence interval for $\mu$ .

Determine t-values -Find the critical t-value that corresponds to $90 \%$ confidence and $\mathrm { n } = 15$ .

Choose the one alternative that best completes the statement or answers the question. -The critical value of a distribution is the value of

Provide an appropriate response. -Assume that the heights of female executives are normally distributed. A random sample of 20 female executives have a mean height of $62.5$ inches and a standard deviation of $3.7$ inches. Construct a $98 \%$ confidence interval for the population variance, $\sigma ^ { 2 }$ .

Provide an appropriate response. -Assume that the heights of bookcases are normally distributed. A random sample of 16 bookcases in one company have a mean height of $67.5$ inches and a standard deviation of $2.9$ inches. Construct a $99 \%$ confidence interval for the population standard deviation, $\sigma$ .

Provide an appropriate response. -A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of $n$ employees produced the following $90 \%$ confidence interval for the proportion of employees who prefer plan A: $( 0.332,0.612 )$ . Identify the point estimate for estimating the true proportion of employees who prefer that plan.

Provide an appropriate response. -When 500 junior college students were surveyed, 120 said that they have previously owned a motorcycle. Find a point estimate for $p$ , the population proportion of students who have previously owned a motorcycle.

Find Critical Values for the Chi-Square Distribution -True or False: The chi-square distribution is a symmetric distribution for all degrees of freedom.