STAT CRUNCH 4

For each problem, determine whether you will use the z- or the t-distribution, or proportion.

A sample of 45 students selected from a large university produced a mean GPA (grade point average) of 2.77 and a standard deviation of 0.38. Make a 95% confidence interval for the mean GPA of all students at this university.

A sample of 46 students produced a mean age of 25 years old with a standard deviation of 2.8 years. Assume that the ages of students is normally distributed, find the 99% confidence interval for the population mean.

A company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 90% confidence level. It is known that the standard deviation of net weights of all 32-ounce packages of Yummy Taste cookies is 0.10 ounces. A sample of 36 packages yielded a mean of 31.9 ounces.

A sample of 1000 families selected from a large city showed that 35% of them make $100,000 or more per year. Find the 94% confidence interval for the proportion of all families living in this city who make $100,000 or more per year.

A sample of 250 auto drivers selected from New York showed that they pay on average $152 auto insurance premium per month with a standard deviation of $38. Make a 98% confidence interval for the mean monthly auto insurance premium paid by all New York auto drivers.

After 784 people were injected with a particular vaccine, 430 experienced side effects. Construct a 95% confidence interval for the proportion of all people who experience side effects after being injected with this vaccine.

A random sample of 12 parking meters in a resort community showed the following incomes for a day.

1. Assume the incomes are normally distributed. Find the 95% confidence interval for the true mean.
2. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.50 $3.00 $2.22 $2.05
3. In a recent study of 43 eighth graders, the mean number of hours per week that they played video games was 22.8 with a population standard deviation of 6.7 hours. Compute the 90% confidence interval for ?.
4. An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the familyàfinancial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level.