AP Stats Inference Method

Mr. Reinecke wants to estimate the proportion of seniors who will go to college next year with 96% confidence and a margin of error of no more than 5%. What size sample does he need to take?

• 422

• 419

• 410

• 400

Mrs. Soto polled 1000 adults and estimated with 90% confidence that the proportion of adults who have dessert after dinner is .75. Ms. Libner thinks that 90% confidence isn't enough and wants to do a 95% confidence. How would a margin of error for 95% compare with a ME for 90% if the same sample size was used?

• It would be smaller because a higher confidence means a smaller MOE

• It would be larger because a higher confidence means a larger MOE

• It would be the same because the sample size is the same

• Won't be able to tell without knowing the true parameter

You want to calculate a 98% confidence interval for a population mean with a sample of n = 20. What is the appropriate t*?

• 2.326

• 2.528

• 2.539

• 2.518

The heights of 5-year old boys are approximately normal. The mean height of a random sample of 37 5-year old boys is found to be 30 inches with a standard deviation of 3 inches. What is the standard error of x̄?

• .493

• 1.32

• 5.77

• 1.96

Mrs. Soto wants to find the sample size needed to find with 95% confidence the mean amount of time her stats students spent on homework during the snow days. The population is approximately normal and the known standard deviation is 6 minutes. How large should the sample size be if she wants a margin of error of +- .5 minutes?

• 553

• 551

• 600

• 601

What would be the name of the confidence interval if constructed in this situation?

• sample p interval for z

• sample z interval for p

• sample t interval for p

• sample p interval for t

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 would NOT be an condition we need to verify before constructing the interval?

• 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 would be the margin of error if you had a 99% confidence?

• 0.022

• 0.0046

• 0.008

• 0.016

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x̄ = 810 grams. This sample mean is an unbiased estimator of the mean weight in the population of all ELBW babies, which means that

• In all possible samples of size 219 from the population, the mean of the values of will equal 810.

• In all possible samples of size 219 from this population, the mean of the values of will equal μ

• As we take larger and larger samples from this population, x̄ will get closer and closer to μ .

• In all possible samples of size 219 from the population, the values of will have a distribution that is close to Normal.

• The person measuring the children’s weights does so without any error.

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.