Confidence Interval with Means Review

As n grows larger, the mean of the sampling distribution of x̄ gets closer to μ.

• True

• False

The distribution of x̄ is approximately normal if the population is normal.

• True

• False

The mean and the standard deviation of the distribution of x̄ are μ and σ/√n respectively.

• True

• False

The larger the value of n, the closer the t distribution is to a z distribution.

• True

• False

Students investigating the packaging of Ruffles Potato Chips, labeled 28.3 grams, randomly selected 50 bags and found a mean weight of 28.1 grams with a standard deviation of 1.4 grams. Assuming the weights are normally distributed, what is the margin of error for the 90% confidence interval?

• a. 0.333

• b. 2.352

• c. 0.329

• d. 2.324

Which statement correctly describes the relation between a t-distribution and a standard normal distribution?

• a. The t distribution has more area in the tails than the standard normal .

• b. The standard normal distribution is centered at 0, while the t-distribution is centered at (n-1).

• c. The t-distribution has a smaller standard deviation than the standard normal distribution.

• d. The standard normal is just another name for the t-distribution.

• e. As the sample size increases, the standard deviation of the t-distribution decreases.

Which statement about the t-distributions is false?

• a. The t-distribution is symmetric.

• b. The standard deviation of the t-distribution approaches –∞ as the degrees of freedom increases.

• c. The t-distribution has a smaller standard deviation than the standard normal distribution.

• d. The t-distribution is centered at zero.

For a random sample from a skewed population, for which of the following sample sizes would the sampling distribution of x̄ be closest to normal in shape?

• a. n = 4

• b. n = 10

• c. n = 25

• d. n = 60

In order for the sampling distribution of the sample mean to be approximately normal, which of the following must be true?

I.The sample size must be large.

II.The population distribution must be normal

• a. I only

• b. II only

• c. Either I or II

• d. Both I and II

• e. Neither I nor II is necessary

Each individual in a random sample of 50 Internet users was asked how many minutes he or she spends online in a typical day. The data was then used to construct a 99% confidence interval for the mean number of minutes spent online in a typical day for all Internet users. The confidence interval was (80, 200) minutes per day. Which of the following is a correct interpretation of the confidence interval?

• a. There is a 99% chance that the mean number of minutes spent online in a typical day by all Internet users is between 80 and 200.

• b. We are 99% confident that the sample mean is between 80 and 200 minutes.

• c. We are 99% confident that the population mean number of minutes spent online in a typical day for all Internet users is between 80 and 200.

• d. 99% of all Internet users will spend between 80 and 200 minutes online in a typical day.

• e. 99% of the people in the sample spent between 80 and 200 minutes online in a day.