AP Stats Confidence Intervals for a Mean

A study of a local high school with 2,000 students tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 253 students in the high school and found a mean of 186 messages sent per day with a standard deviation of 65 messages. What would the critical value for an 80% confidence interval be in this situation?

A study of a large local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 97 AP students in the high school and found a mean savings of 4100 dollars with a standard deviation of 500 dollars.

Would you use a One Sample z Interval or a One Sample t Interval for this situation?

• One Sample z Interval

• One Sample t Interval

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 25 graduating seniors and found the mean score to be 471 with a standard deviation of 83.

Would you use a one sample z interval or a one sample t interval in this situation?

• One Sample z Interval

• One Sample t Interval

A study of a local high school with 2,000 students tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 253 students in the high school and found a mean of 186 messages sent per day with a standard deviation of 65 messages.

Would you use a one sample z interval or a one sample t interval for this situation?

• One Sample z Interval

• One Sample t Interval

You want to compute a 90% confidence interval for the mean difference in height for mothers and their adult daughters using a random sample of 30 mothers who have an adult daughter. What critical value should you use for this interval? (Enter 3 decimal places)

Answer explanation

The 𝑡* value for 90% confidence and df = 29 is 𝑡* = 1.699.

The makers of a specialty brand of bottled water claim that their “mini” bottles contain 8 ounces of water. To investigate this claim, a consumer advocate randomly selected a sample of 10 bottles and carefully measured the amount of water in each bottle. The mean volume was 7.98 ounces and the 95% confidence interval for true mean volume is 7.93 to 8.03 ounces.

Complete this statement.

Because ​​ (a)   ​ (b)   the interval, there ​​ (c)   convincing evidence that their claim is incorrect.

• 8

• is

• is not

• 0

• 7.98

Answer explanation

Because 8 is in the interval, there is not convincing evidence that their claim is incorrect.

The weights (in pounds) of three adult males are 160, 215, and 195. What is the standard error of the mean for these data?

• 27.84

• 22.73

• 13.13

• 16.07

• 190

We want to construct a one-sample 𝑡 interval for a population mean using data from a population with unknown shape. In which of the following circumstances would it be inappropriate to construct the interval based on an SRS of size 14 from the population?

• A boxplot shows that the values above the median are much more variable than the values below the median.

• A stemplot of the data is roughly bell-shaped.

• The sample standard deviation is small.

• The sample standard deviation is large.

• A histogram of the data shows slight skewness.

Answer explanation

We should not use 𝑡 procedures when the sample size is small (𝑛<30) and the distribution is skewed (the values above the median are much more variable than the values below the median).

A 90% confidence interval for the mean 𝜇 of a population is computed from a random sample and is found to be 90 ± 30. Which of the following 𝑐𝑜𝑢𝑙𝑑 be the 95% confidence interval based on the same data?

• 90 ± 21

• Without knowing the sample size, any of the above answers could be the 95% confidence interval.

• 90 ± 39

• 90 ± 70

• 90 ± 30

Answer explanation

The margin of error for a confidence interval with 95% confidence will have a larger margin of error, but not more than double the margin of error for a 90% confidence interval.

Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours. For a random sample of 45 seniors without part time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours. Assuming the conditions are met, which of the following is the correct standard error for a 95% confidence interval for a difference in the population means?

• 
• 
• 
• 
• 

Answer explanation

Be careful to not confuse the means with the standard deviations in this expression.