Meaghan wants to study her friends’ drinking habits. Meaghan knows that people drink, on average, 0.6 alcoholic beverages per day, with standard deviation 0.5. Meaghan investigates how many alcoholic drinks her 49 friends drink. Meaghan finds that her group of friends drinks, on average, 0.7 alcoholic beverages per day. Do Meaghan’s friends’ drinking habits differ significantly from people in general. In the provided space, type in the answers to the following questions.

1. Which statistical test would you use to solve this problem?

2. State the null and alternative hypotheses in words.

3. Locate the critical value that defines the critical region.

4. Calculate your statistic.

5. Make a decision with respect to the null hypothesis.

6. Write a concluding sentence in everyday language.

7. Calculate and evaluate Cohen’s d.

On Arvala-7, Jawas are notorious for stealing parts from unattended vehicles. The number of part thefts over a one-month period in 40 randomly selected regional zones have a mean of 5.5 thefts and a standard deviation of 5.8 thefts.

1) Find the standard error for the number of parts thefts on Arvala-7.

2) Construct a 95% confidence interval for the true mean number of such thefts.

3) Interpret the confidence interval by stating your answer in a carefully worded sentence.

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where X1 is normally distributed with a mean of 113 cm and a standard deviation of 5 cm, X2 is normally distributed with a mean of 245 cm and a standard deviation of 10 cm, and X3 is normally distributed with a mean of 98 cm and a standard deviation of 2 cm.

1. Find the mean perimeter of the trapezoid.

2. Suppose X1, X2, and X3 are independent of each other. Find the variance of the perimeter of the trapezoid.

3. Suppose that the covariance between X1 and X2 is 35, but X3 is independent of both X1 and X2. Find the variance of the perimeter of the trapezoid.

The proportion of the standard normal curve that falls between the mean and a Z-score of 2.15 is .4842.

true or false

According to a Gallup poll, 11.55% of American adults have diabetes. A researcher wonders if the rate in her area is higher than the national rate. She surveys 150 adults in her area and finds that 21 of them have diabetes.

1) If the region had the same rate of diabetes as the rest of the country, how many would we expect to have diabetes?

2) Suppose you are testing the hypothesis that the diabetes rate in this area differs from the national rate. State the null and alternative hypotheses for such a test.

3) State the value of the test statistic and the p-value.

4) Use a 0.05 significance level to make a decision about the null hypothesis and state your conclusion in context.

Constructing Confidence Intervals In Exercises 45 and 46, use the information to construct 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

45. DVR and Other Time-Shifted Viewing A group of researchers estimates the mean length of time (in minutes) the average U.S. adult spends watching television using digital video recorders (DVRs) and other forms of time-shifted television each day. To do so, the group takes a random sample of 30 U.S. adults and obtains the times (in minutes) below.

29 12 23 24 33 24 28 31 18 27 27 32 17 13 17 12 21 32 26 16 28 28 21 24 29 13 20 13 21 27  

From past studies, the research council assumes that s is 6.5 minutes. (Adapted from the Nielsen Company)

46. Sodium Chloride Concentrations The sodium chloride concentrations (in grams per liter) for 36 randomly selected seawater samples are listed. Assume that s is 7.61 grams per liter.

30.63 33.47 26.76 15.23 13.21 10.57 16.57 27.32 27.06 15.07 28.98 34.66 10.22 22.43 17.33 28.40 35.70 14.09 11.77 33.60 27.09 26.78 22.39 30.35 11.83 13.05 22.22 13.45 18.86 24.92 32.86 31.10 18.84 10.86 15.69 22.35

describe the process of hypothesis test regarding the difference between two population proportions

An observational study was conducted to find out if eating whole-wheat products was associated with a reduction in body mass index (BMI) for children. The measure of interest was the difference between population mean BMI for children who eat whole wheat products and children who don’t.

a) Write the null and alternative hypotheses for this situation.

b) Describe what a type 1 error would be in this situation.

c) Describe what a type 2 error would be in this situation.

d) Which type of error do you think is more serious in this situation? (There is no correct answer; it is your reasoning that counts.)

Two players play each other in a pool tournament of "Solids and Stripes". The first player to win two games wins the tournament. In the game of "Solids and Stripes", it is equally likely that a player will be assigned solid balls or striped balls. Assume that 1) one-half of the balls are solids and the other half are stripes, 2) the two players have the same skill: each with a 0.5 probability of winning, 3) there are no ties, and 4) the tournament is concluded once a player has won two games. In a tournament, what is the probability that a player is assigned the same ball design (i.e., solids or stripes) throughout the tournament?

6. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 38 preferred the Half Pint lager, 32 preferred the XXX lager, and 10 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that the production of the premium lagers matches these consumer preferences using a 0.05 level of significance.

- State the value of the test statistic. (Round your answer to two decimal places.)

- State the decision to retain or reject the null hypothesis.

7. A psychologist studying addiction tests whether cravings for cocaine and relapse are independent. The following table lists the observed frequencies in the small sample of people who use drugs.

Part A) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)

Decide whether to retain or reject the null hypothesis.

Part B) Compute effect size using ϕ and Cramer's V. Hint: Both should give the same estimate of effect size. (If necessary, round your intermediate steps to two or more decimal places. Round your answers to two decimal places.)

For each of the following examples, state whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate, and state the degrees of freedom (df) for the test.

Part A) An instructor tests whether class attendance (low, high) and grade point average (low, average, high) are independent.

- State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

- State the degrees of freedom for the test. df =

Part B) A student tests whether the professor's speaking style (monotone, dynamic) and student interest (low, average, high) are independent.

- State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

- State the degrees of freedom for the test. df =

Part C) A health psychologist records the number of below average, average, overweight, and obese individuals in a sample of college students.

- State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

- State the degrees of freedom for the test. df =

Part D) A personality psychologist compares the number of single mothers with Type A or Type B personality traits.

- State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

- State the degrees of freedom for the test. df =

Question 1

1. The Goodness of Fit test and the Test of Independence are two forms of which of the following test? (2 points)
   1. Regression analysis
   2. Correlation analysis
   3. Chi-square analysis
   4. Independent samples t-test
   5. Related samples t-test
2. We can make cause-and-effect statements when: (2 points)
   1. We run correlations to see how two variables are related to one another
   2. We use experimental manipulations (i.e., through the manipulation of the independent variable)
3. What type of question do chi-squares answer? (2 points)
   1. Can we predict variable Y from variable X?
   2. What is the relationship between two variables? Are these variables associated with one another? Is there a difference in frequencies across groups?
   3. Are there significant differences in the outcome variable across groups? Are there significant differences across group means?  
4. What type of question do t-tests answer? (2 points)
   1. Can we predict variable Y from variable X?
   2. What is the relationship between two variables? Are these variables associated with one another?
   3. Are there significant differences in the outcome variable across groups? Are there significant differences across group means?  

1) What was the margin of error for the confidence interval for gasoline mileage of make 2?

2) What was the lower 95% confidence limit for make 2 mileage?

3) What was the upper 95% confidence limit for make 2 mileage?

4) What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage?

DATAfile: HongKongMeals

You may need to use the appropriate appendix table or technology to answer this question.

The mean cost of a meal for two in a midrange restaurant in City A is $44. How do prices for comparable meals in Hong Kong compare? The file HongKongMeals contains the costs for a sample of 42 recent meals for two in Hong Kong midrange restaurants.

(a)

With 95% confidence, what is the margin of error for the estimated mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answer to the nearest cent.)

$

(b)

What is the 95% confidence interval estimate of the population mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answers to the nearest cent.)

$  to $

(c)

How do prices for meals for two in mid-range restaurants in Hong Kong compare to prices for comparable meals in City A restaurants?

The mean cost for a mid-range meal for two in City A is  ---Select--- within higher than the upper limit of below the lower limit of the 95% confidence interval for comparable meals in Hong Kong. This suggests mean cost of comparable meals in Hong Kong is  ---Select--- less than possibly the same as greater than  in City A.