8.2 Day 2 Practice

A study found that in a random sample of 44 subjects, 9 of them agree that children under 6 shouldn’t be taken to nice restaurants.

The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the true proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• We are 95% confident that the true proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size

• decreasing the confidence level, decreasing the sample size

• increasing the confidence level, decreasing the sample size

• decreasing the confidence level, increasing the sample size.

A random sample of 110 GBW students found that 53 of them were in possession of a pencil. What is p-hat for this sample?

• 0.53

• 53

• 0.48

• 1

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card. Identify the name of the confidence interval for the proportion of adults with credit cards that carry a balance of $1000 or more.

• z interval

• 1 proportion z interval

• 1 sample t interval for p

• 1 proportion t interval

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

Which of the following would NOT be a condition we need to verify before constructing the interval for the proportion of all adults that have a balance of $1000 or more?

• np̂ ≥ 10 and n(1-p̂) ≥ 10

• n ≥ 30

• 10% condition

• random sample

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What is the margin of error for a 99% confidence interval for the proportion of all adults that have a balance of $1000 or more??

• 0.022

• 0.0046

• 0.008

• 0.016

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What symbol describes the parameter?

• μ

• p

• p̂

• x̄

Why is it important to check the 10% condition before calculating probabilities involving x̄?

• To reduce the variability of the sampling distribution of x̄

• To ensure that the distribution of x̄ is approximately Normal

• To ensure that we can generalize the results to a larger population

• To ensure that x̄ will be an unbiased estimator of μ.

• To ensure that the observations in the sample are close to independent since we are sampling without replacement.

One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

• z can be used only for large samples

• z requires that you know the population standard deviation

• z requires that you can regard your data as an SRS from the population

• z requires that the sample size is at most 10% of the population size

• a z critical value will lead to a wider interval than a t critical value

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large of a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%.

• 1201

• 13

• 600

• 601