Find the sample proportions and test statistic for equal proportions. Find the $p$-value.

Home equity loan default rates in two banks: $x_1=36, n_1=480, x_2=26, n_2=520$, $\alpha=.05$, right-tailed test.

Calculate the test statistic and $p$-value for a test of equal population proportions. What is your conclusion?

Right-tailed test, $\alpha=.05, x_1=276, n_1=300, x_2=440, n_2=500$

Calculate the test statistic and $p$-value for a test of equal population proportions. What is your conclusion?

Left-tailed test, $\alpha=.10, x_1=28, n_1=336, x_2=14, n_2=112$

Calculate the test statistic and $p$-value for a test of equal population proportions. What is your conclusion?

Two-tailed test, $\alpha=.05, x_1=52, n_1=80, x_2=56, n_2=70$

The Cat is a high-speed catamaran auto ferry that operates between Bar Harbor, Maine, and Yarmouth, Nova Scotia. The Cat can make the $138\text{-mile}$ trip in about $2 \frac{1}{2}$ hours. Find the catamaran speed for this trip.

Calculate the test statistic and $p$-value for a test of equal population proportions. What is your conclusion?

Left-tailed test, $\alpha=.05, x_1=36, n_1=80, x_2=66, n_2=120$

Calculate the test statistic and $p$-value for a test of equal population proportions. What is your conclusion?

Right-tailed test, $\alpha=.10, x_1=228, n_1=240, x_2=703, n_2=760$

Match each statement to the correct property of an estimator (unbiased, consistent, efficient):

a. The estimator “collapses” on the true parameter as n increases.

b. The estimator has a relatively small variance.

c. The expected value of the estimator is the true parameter.

SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

What percentage of SAT scores is between 401 and 629?

Is $1900$ SAT score a good score on a SAT test if the mean score is $1240$ and the standard deviation is $270$ and SAT scores are distributed normally ?

Do a two-sample test for equality of means assuming equal variances. Calculate the $p$-value.

Comparison of GPA for randomly chosen college juniors and seniors: $\tilde{x_1}$ = 139, $s_1$ = 2.8, $n_1$ = 12, $\tilde{x_2}$ = 137, $s_2$ = 2.7, $n_2$ = 17, $\alpha$ = .025, right-tailed test.

Why do we say that two- sample tests have a built-in point of reference?

Do a two-sample test for equality of means assuming equal variances. Calculate the $p$-value.

Comparison of GPA for randomly chosen college juniors and seniors: $\tilde{x_1}$ = 15, $s_1$ = 5, $n_1$ = 22, $\tilde{x_2}$ = 18, $s_2$ = 7, $n_2$ = 19, $\alpha$ = .025, two-tailed test.

Do a two-sample test for equality of means assuming equal variances. Calculate the $p$-value.

Comparison of GPA for randomly chosen college juniors and seniors: $\tilde{x_1}$ = 3.05, $s_1$ = .20, $n_1$ = 15,$\tilde{x_2}$ = 3.25, $s_2$ = .30, $n_2$ = 15, $\alpha$ = .025, left-tailed test.