The P-value for a two-sided test of the null hypothesis : population mean =15 is 0.03.

Does the 99% confidence interval for $\mu$ include 15 ? Why or why not?

A blogger claims that U.S. adults drink an average of five 8-ounce glasses (that's 40 ounces ) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers. Do we have convincing evidence that the amount of water U.S. children drink per day differs from 40 ounces? Justify your answer.

A blogger claims that U.S. adults drink an average of five 8-ounce glasses (that's 40 ounces ) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

A Type I error is defined to be the probability of
(a) failing to reject a true null hypothesis.
(b) failing to reject a false null hypothesis.
(c) rejecting a false null hypothesis.
(d) rejecting a true null hypothesis.

In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for $14$ people, based on means and standard deviations given in the article.

$$\begin{array}{rrrrrrr} \hline 18.2 & 24.8 & 3.9 & 20.0 & 17.1 & 8.8 & 13.4\\ 17.3 & 33.8 & 29.7 & 8.5 & 31.2 & 19.3 & 15.1\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ A boxplot shows these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain.

$\textbf{b.}\hspace{10pt}$ If appropriate, perform a hypothesis test to determine whether the mean weight loss is greater than $10$ pounds. Use the $\alpha = 0.05$ level of significance. What do you conclude?

The following situation calls for a significance test. State the appropriate null hypothesis

$$H_0$$

and alternative hypothesis

$$H_a.$$

Be sure to define your parameter. Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Jordan suspects that Jordanian children are at risk of anemia. He measures a random sample of 50 children.

Refer to the previous exercise where the germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of corn usually has a germination rate of 0.80. As their science project, a group of students wants to see if spraying seeds with a chemical known to increase germination rates will increase the germination rate of this variety of corn. They spray a random sample of 400 seeds with the chemical, and 339 of the seeds germinate. You would like to perform a test at the $\alpha$=0.05 significance level of $H_0$: p=0.80 versus $H_a$: p>0.80, where p= the true proportion of this variety of corn that will germinate when sprayed with the chemical.

Which type of error-a Type I error or a Type II error-could you have made in the last part of the said exercise? Explain your answer.

Which of the following is the primary purpose of the DSM-5? a. Describing mental disorders. b. Selecting appropriate psychological therapies for mental disorders. c. Placing mental disorders in their appropriate cultural context d. Selecting appropriate medicines to treat mental disorders. e. Understanding the causes of mental disorders.

A Gallup Poll found that 59% of the people in its sample said "Yes" when asked, "Would you like to lose weight?" Gallup announced: "For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is

$$\pm3$$

percentage points." Does this interval provide convincing evidence that the actual proportion of U.S. adults who would say they want to lose weight differs from 0.55? Justify your answer.

Why does the Large Counts condition need to be meet?

What are the two possible explanations when a basketball player who claims to be an 80% free throw shooter makes only 64% of free throws taken in 50 attempts?

True/False: If the sample size is small and the shape of the population distribution is unknown, the Normal/ Large Sample condition is met if a graph of the sample data shows no strong skewness or outliers.

A veterinarian claims that the mean weight of adult German shepherd dogs is $75$ pounds. A test is made of $H_0: \mu = 75$ versus $H_1: \mu \ne 75$. The null hypothesis is not rejected. State an appropriate conclusion.

True/False: When a researcher plans to make a conclusion based on a significance test, the significance level should be stated before the data are produced.