Construct the indicated confidence interval for the population mean $$\mu$$ .

$$c=0.95,\ \ \overline{x}=645,\ \ s=31,\ n=16$$  

In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of $22.50. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expenses is normally shaped.

Construct a 95% confidence interval for the population mean $$\mu$$ . Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.

A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean.

Construct a 98% confidence interval for the population mean $$\mu$$  . Assume the population has a normal distribution. A study of 14 bowlers showed that their average score was 192 with a standard deviation of 8.

The grade point averages for 10 randomly selected high school students are listed below. Assume the grade point averages are normally distributed.

2.0 3.2 1.8 2.9. 0.9. 4.0 3.3 2.9 3.6 0.8

Find a 98% confidence interval for this data.

When 410 college students were surveyed, 150 said they own their own car. Find a point estimate p the population proportion of students who own their cars.

A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.

A researcher at a major hospital wishes to estimate the proportion of the U.S. adult population that has high blood pressure. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true population by more than 5%.

A survey of 2450 golfers showed that 281 of them are left-handed. Construct a 98% confidence interval for the proportion of golfers that are left-handed.

A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed to be 98% confident that the sample proportion will not differ from the true population by more than 3%.

In a sample of 10 randomly selected women, it found that their mean height was 63.4 inches. From previous studies, it is assume that the standard deviation $$\sigma$$  is 2.4 and that the population of height measurements is normally distributed. Construct a 95% confidence interval for the population mean.

Construct a 99% confidence interval for the population mean $$\mu$$ . Assume the population has a normal distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

A survey of 400 non-fatal accidents showed that 181 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.