A hypothesis test is conducted with a $0.05$ significance level so that there is a 0.05 chance of making the mistake of rejecting a true null hypothesis. If two different independent hypothesis tests are conducted with a $0.05$ significance level, what is the possibility that both conclusions are mistakes of rejecting a true null hypothesis?

In each part, give the value of the standardized statistic (z-score) for the sample mean:

a. $\overline{x}$ = 74, $\mu$ = 72, $\sigma$ = 10, n = 25.

b. $\overline{x}$ = 70, $\mu$ = 72, $\sigma$ = 10, n = 25.

c. $\overline{x}$ = 92, $\mu$ = 100, $\sigma$ = 16, n = 4.

d. $\overline{x}$ = 92, $\mu$ = 100, $\sigma$ = 16, n = 64.

e. $\overline{x}$ = 10.15 , $\mu$ = 10.0, $\sigma$ = 5, n = 10,000.

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

a) Compute the standardized residual for each type of card.

The t-test is used to test the joint hypotheses concerning all individual regression coefficients. True or False?

A teacher gives a test in which the average of the test scores is 68 and the standard deviation is 14. Realizing that the test was probably too difficult, the teacher decides to scale the tests by adding 10 points to all scores. What is the mean and standard deviation of the scaled test scores?

Use the Comparison Tests for Convergence or Divergence to determine whether each series converges or diverges. $\sum_{k=2}^{\infty} \frac{4^{k}}{7^{k}+1}$: by comparing it with $\sum_{k=2}^{\infty}\left(\frac{4}{7}\right)^{k}$

Urine tests that detect steroid use by athletes are being advocated by many high school coaches. Interview several coaches to determine their attitudes toward steroid testing. Write an article for your school newspaper that discusses your findings and explains how steroids affect the body.

The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the person’s saliva becomes more acidic. After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?

When a test for steroids is given to soccer players, 98% of the players taking steroids test positive and 12% of the players not taking steroids test positive. Suppose that 5% of soccer players take steroids. What is the probability that a soccer player who tests positive takes steroids?

Suppose a

$$3 \times 3$$

factorial experiment is conducted with three replications. Assume that SS(Total) = 1,000. For each of the following scenarios, form an ANOVA table, conduct the appropriate tests, and interpret the results: SS( A ) is 40%, SS( B ) is 40%, and SS( AB ) is 10% of SS(Total).

Briefly describe what you regard as the most useful tips for taking each of the following kinds of tests.

$$\begin{array} { l } { \cdot \text { multiple-choice } } \\ { \cdot \text { true-false } } \\ { \cdot \text { short-answer } } \\ { \cdot \text { essay } }\end{array}$$

Determine an interval in which all real zeros of each function must lie. Explain your reasoning using the upper and lower bound tests. than find all the real zeros. $g(x)=2 x^{4}+4 x^{3}-18 x^{2}-4 x16$

Use a significance level of $0.05$ for all tests below.

Use the most recent NFL season for your data. For each team, find the quarterback rating for the number one quarterback. Test the claim that the mean quarterback rating for a number one quarterback is more than 80 .

Determine all rational zeroes of the functions given and use them to express the function in factored form. Use the factored form to state all zeroes of $f$. Begin by applying the tests for 1 and $-1$.

$$r(x)=3 x^4+4 x^3+8 x^2+16 x-16$$