• 10.7 When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and 1,041 for the group that thought about the organic fruit salad. (Data extracted from “Drilling Down, Sizing Up a Cheeseburger's Caloric Heft,” The New York Times, October 4, 2010, p. B2.) Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.

• a. State the null and alternative hypotheses if you want to determine whether the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

• b. In the context of this study, what is the meaning of the Type I error?

• c. In the context of this study, what is the meaning of the Type II error?

• d. At the 0.01 level of significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first?

SHOW EXCEL FUNCTIONS USED TO ANSWER.

A school psychologist wishes to determine whether a new antismoking film actually reduces the daily consumption of cigarettes by teenage smokers. The mean daily cigarette consumption is calculated for each eight teenage smokers during the month before and the month after the film presentation, with the following results:

MEAN DAILY CIGARETTE CONSUMPTION

(Note: when deciding on the form of the alternative hypothesis, H1, remember that a positive difference score (D=X1-X2) reflects a decline in cigarette consumption.)

Using t, test the null hypothesis at the .05 level of significance.

A)What is the research problem in this scenario?

B)Which of the following is the appropriate pair of statistical hypotheses for this study?

C)Compute the degrees of freedom for this scenario.

D)What is the decision rule in this scenario?

E)Calculate the value of the t test.

F)What is the decision about the null hypothesis in this scenario?

H)What is the interpretation in this scenario?

I)If appropriate (because the null hypothesis was rejected), construct a 95 percent confidence interval for the true population mean for all difference scores and use Cohen’s d to obtain a standardized of the effect size. Lower bound, upper bound, or 0 if null hypothesis is retained

J)Enter the estimate of the standardized effect size (Cohen’s d).

K)What might be done to improve the design of this experiment?

(1 point) A hockey player is to take 3 shots on a certain goalie. The probability he will score a goal on his first shot is 0.35. If he scores on his first shot, the chance he will score on his second shot increases by 0.1; if he misses, the chance that he scores on his second shot decreases by 0.1. This pattern continues to on his third shot: If the player scores on his second shot, the probability he will score on his third shot increases by another 0.1; should he not score on his second shot, the probability of scoring on the third shot decreases by another 0.1.

A random variable ?X counts the number of goals this hockey player scores.

(a) Complete the probability distribution of ?X below. Use four decimals in each of your entries.

(b) How many goals would you expect this hockey player to score? Enter your answer to four decimals.

?(?)=E(X)=

equation editor

Equation Editor

(c) Compute the standard deviation the random variable ?X. Enter your answer to two decimals.

??(?)=SD(X)=

equation editor

Equation Editor

A researcher is concerned that the true

population mean could be as much as 4.8 greater

than the accepted population mean, but the

researchers hypothesis test fails to find a

significant difference. The power for this study

was 0.5, the researcher probably should

A) accept the outcome and move on

B) repeat the experiment with a smaller α

C) repeat the experiment with a larger α

D) repeat the experiment with a larger n

E) repeat the experiment and hope that the next sample

mean is significantly different than the hypothesized

mean.

Failing to observe a treatment affect

for Rogaine, when in reality Rogaine reduces

hair loss, would be...

A) impossible

B) an error with probability equal to α

C) an error with probability equal to β

D) an error with probability equal to 1-β

Use EXCEL and screenshot all steps

A random sample of 89 tourists in Chattanooga showed that they spent an average of $2860 (in a week) with a standard deviation of $126; and a sample of 64 tourists in Orlando showed that they spent an average of $2935 (in a week) with a standard deviation of $138. We are interested in determining if there is any significant difference between the average expenditures of all the tourists who visited the two cities.

Determine the degrees of freedom for this test.

Select one:

a. 152

b. 128

c. 153

d. 127

Compute the test statistic.

Select one:

a. 0.157

b. -0.157

c. 3.438

d. -3.438

What is your conclusion? Let α = .05.

Select one:

a. Can not make a conclusion.

b. p-value > .05, can not reject H0.

c. p-value < .005, reject H0. There is a significant difference.

d. p-value < .05, reject H0. There is a significant difference.

The diameter of a brand of​ ping-pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample of 16 ​ping-pong balls is selected. Complete parts​ (a) through​ (d). What is the probability that the sample is between 1.28 and 1.3 ​inches?

According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question.

A) At least 3 flights are not on time.

B) At the most 8 flights are on time.

C) In between 6 and 9 flights are on time.

What are the advantage and disadvantage of assuming normally distributed returns in meanvariance analysis?

Time spent using​ e-mail per session is normally​ distributed, with mu equals 7 minutes and sigma equals 2 minutes. Assume that the time spent per session is normally distributed. Complete parts​ (a) through​ (d). If you select a random sample of 200 ​sessions, what is the probability that the sample mean is between 6.8 and 7.2 ​minutes?

suppose that you have data on many (say 1,000) randomly selected employed country's  residents. FURTHER DETAILS GIVEN IN THE END OF THE QUESTIONS

a) Explain how you would test whether, holding everything else constant, females earn less than males.

b) Explain how you would measure the payoff to someone becoming bilingual if her mother tongue is i) French, ii) English.

c) Does including both X₃ and X₄ in this regression model have the potential to show any "problems" when estimating your regression model? Explain. Would eliminating one of them potentially cause other problems? Explain

d) Can you use this model to test if the influence of on-the-job experience is greater for males than females? Why or why not? If not, how would you need to change the model to test whether the influence of on the job experience is greater for males than females?

FURTHER DETAILS:

Consider the following linear regression model "explaining" salaries in the Country:

Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + β₅D₁ + β₆D₂ + β₇D₃ + µ

where: Y = salary,

X₁ = years of education,

X₂ = innate ability (proxied by IQ test results)

X₃ = years of on the job experience

X₄ = age

D₁ = a dummy variable for gender (= 1 for males, 0 for females)

D₂ = 1 for uni-lingual French speakers

D₃ = 1 for uni-lingual English speakers

Use data from Excel to complete problems 3.1 and 3.2. When you open the file look at the tabs on the bottom left. You will use the data from the “Class_LabScores” tab to answer these questions.

3.1. Dr. Wallace teaches three statistics labs at three different times of day (1 - morning, 2 - noon, 3 - night). She is curious to find out whether or not time of day is related to student scores on the lab assignments. Frequency distribution tables for each of her three lab classes appear on the “Class_LabScores” tab in the Excel file. Please calculate the following:

Mean for Morning Class 1:

Mean for Noon Class 2:

Mean for Night Class 3:

3.2 Dr. Wallace is preparing a summary of her teaching experience in the statistics lab classes. She only wants to use one number to represent student performance in those classes, so she’ll need to calculate one mean. In addition, she wants to be fair and make sure that every student’s lab score contributes equally to the overall mean. In order to do this, she needs to calculate the weighted mean. Please calculate the following and show work:

Weighted mean for her statistics classes:

The objective of the question is to test the Hypothesis If the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A. First you must find the mean and standard deviations. Then perform and list the complete required steps for the TWO required Hypothesis tests and use the P-Value as a rejection Rule for both tests.

One Hypothesis test is an F test for the equality of the variances of travel Times and the second test is a T test for the equality of the means of travel times in minutes. The F test must be performed first in order to select either Case1 or Case 2 for the T-test.

Recorded Time values in minutes from point A to point B in minutes: 32, 34, 51, 30, 29, 35, 36, 29, 32, 29, 33, 32, 29, 30, 33, 30, 30, 33, 30, 31, 35, 35, 34, 33, 31, 34, 30, 30, 29, 34, 32, 35, 29, 30, 32, 30, 33, 31

n_A=38

Recorded Time values in minutes from point B to point A in minutes: 36, 28, 48, 28, 27, 54, 34, 29, 26, 34, 33, 42, 29, 34, 31, 4, 27, 42, 28, 45, 26, 43, 32, 30, 27, 29, 29, 35, 26, 31, 28, 27, 28, 32, 41, 34, 28, 31

n_B=38

Describe some of the benefits of using a survey design in quantitative research.