2) A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 89.7% for the medical students admitted through special programs. Be sure to enter at least 4 digits of accuracy for this problem!

If 9 of the students from the special programs are randomly selected, find the probability that at least 8 of them graduated.         prob = -------- At least 4 digits!

If 9 of the students from the special programs are randomly selected, find the probability that exactly 6 of them graduated. prob = ------------ At least 4 digits!

Would it be unusual to randomly select 9 students from the special programs and get exactly 6 that graduate?

no, it is not unusual

yes, it is unusual

If 9 of the students from the special programs are randomly selected, find the probability that at most 6 of them graduated. prob = --------------At least 4 digits!

Would it be unusual to randomly select 9 students from the special programs and get at most 6 that graduate?

yes, it is unusual

no, it is not unusual

Would it be unusual to randomly select 9 students from the special programs and get only 6 that graduate?

No, it is not unusual

Yes, it is unusual

TABLE 11- 4

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields, 5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomized design, the results are presented in the table that follows.

True or False: Referring to Table 11- 4, the decision made at 0.005 level of significance implies that all 3 means are significantly different.

True

False

An investor believes that investing in domestic and international stocks will give a difference in the mean rate of return. They take two random samples of 15 months over the past 30 years and find the following rates of return from a selection of domestic (Group 1) and international (Group 2) investments. Can they conclude that there is a difference at the 0.10 level of significance? Assume the data is normally distributed with unequal variances. Use a confidence interval method. Round to 4 decimal places.

Average Group 1 = 2.1234, SD Group 1 = 4.8765, n1 = 15

Average Group 2 = 3.0945, SD Group 2 = 5.1115, n2 = 15

______ < μ₁ - μ₂ < __________

1- From the 2008 General Social Survey, females and males were asked about the number of hours a day that the subject watched TV. Females (n = 698) reported a mean of 3.08 hours with a standard deviation of 2.70 hours. Males (n = 626) reported a mean of 2.87 hours with a standard deviation of 2.61 hours. Test that the mean hours of TV watched by men and women is different from zero at the 5% significance level.

(A) What are the null and alternative hypotheses?

(B) Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?

a) it is a two-sided test. Thus, the tcritis ±1.960.

b) it is a two-sided test. Thus, the tcrit is ±1.645.

c) A one-sided-test with tcrit = 1.96

d) A one-sided test with tcrit = -1.96

(C.1) Calculate the appropriate test statistic. What is the standard error you calculated?

(C.2) Calculate the appropriate test statistic. What is the test statistic you calculated?

(D) Calculate the corresponding p-value from the appropriate table or online calculator.

(E) What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

(F.1) Construct a 95% confidence interval around the difference-in-means estimate. Find the lower bound of the interval you calculated. (In this case, be sure to use the standard error you calculated when determining the test statistic that uses information about the population proportion.)

(F.2) Construct a 95% confidence interval around the difference-in-means estimate. Find the upper bound of the interval you calculated. (In this case, be sure to use the standard error you calculated when determining the test statistic that uses information about the population proportion.)

(G) How would you interpret the confidence interval?

a) We can be 95% confident that the true mean difference in hours of TV watched per week by males and females in the population falls between lower bound and upper bound.

b) We can not be 95% confident that the true mean difference in hours of TV watched per week by males and females in the population falls between lower bound and upper bound.

STEP 3: You will analyze your data and compute the following statistics for each group:

1) The Mean and standard deviation of the number of seconds the subject stayed balanced

2) The Median number of days per week exercised

3) The Mode of the favorite exercise

4) The 90% confidence interval of the mean

Research into the relationship between hours of study and grades shows widely different conclusions. A recent survey of graduates who wrote the Graduate Management Admissions Test (GMAT) had the following results.

Hours

Studied [Average Score]

(Midpoint)  

40 220

50 310

65 350

75 440

85 560

105 670

95 700

a) Run the regression analysis in Excel on this data. Include your output with your answer. (Note: You may calculate by hand if you prefer).

b) What is the regression equation for this relationship?

c) Use the regression equation to predict the average score for each category of hours studied.

d) Plot the original data and the regression line on a scatter gram. (You may use Excel).

e) How accurate is this regression at predicting GMAT scores based on hours studied? Explain.

f) Use the t statistic to determine whether the Correlation Coefficient is “significant” at the 95% confidence level.

Suppose 243 subjects are treated with a drug that is used to treat pain and 54 of them developed nausea. Use a 0.05 significance level to test the claim that more than 20%​ of users develop nausea.

Question 5: (Marks: 5)

A group of students compared the number of times they have been to the movies in the past year. The following table illustrates how many times each person went to the movie theatre in each month. You need to show your work.

1. By comparing modes, which person went to the movies the least per month?

2. By comparing medians, which person went to the movies the most per month?

3. Rank the students in order of most movies seen to least movies seen by comparing their means.

4. Which month, by comparing the means of movies seen in each month, is the most popular movie-watching month?

5. By comparing medians, which month is the least popular month?

A computer random number generator was used to generate 750 random digits (0,1,...,9). The observed frequences of the digits are given in the table below.

Test the claim that all the outcomes are equally likely using the significance level α=0.05α=0.05.
The expected frequency of each outcome is E=

The test statistic is χ2=

The p-value is

Is there sufficient evidence to warrant the rejection of the claim that all the outcomes are equally likely?
A. No
B. Yes

Question 4: (Marks: 3)

The following table represents the percentage of teenagers in some selected countries who have used marijuana and the percentage who have used other drugs.

1. Determine the correlation coefficient, rounded to two decimal places, between the percentage of teenagers who have used marijuana and the percentage who have used other drugs. Show your work.

2. Does the following statement make sense? Explain your answer.

“I found a positive correlation for the data presented in the table relating the percentage of teenagers in various countries who have used marijuana and the percentage who have used other drugs. I concluded that using marijuana causes the use of other drugs.”

A manufacturer wants to compare the number of defects on the day shift with the number on the evening shift. A sample of production from recent shifts showed the following defects:

Day Shift 6 9 8 7 10 8

Evening Shift 9 11 8 12 10 13 15 10

The objective is to determine whether the mean number of defects on the night shift is greater than the mean number on the day shift at the 95% confidence level.

a) State the null and alternate hypotheses.

b) What is the level of significance?

c) What is the test statistic?

d) What is the decision rule?

e) Use the Excel Data Analysis pack to analyze the problem. Include the output with your answer. (Note: You may calculate by hand if you prefer).

f) What is your conclusion? Explain.

g) Does the decision change at the 99% confidence level?

A researcher compares the effectiveness of two different instructional methods. A random sample of 78 students using Method 1 produces a testing average of 89.5 with a standard deviation of 16.8. A sample of 117 students using Method 2 produces a testing average of 55.9 with a standard deviation of 8.2. Construct a 99% confidence interval for the true difference in testing averages between the two methods. Round the endpoints of your interval to the nearest tenth if necessary. Show all work.

A recent survey on the usage of cosmetics among youth provided the following data:

Year: 2004; Sample size: 5000; Youth who use cosmetics: 36%
Year: 2014; Sample size: 4250; Youth who use cosmetics: 47%

Construct a 99% confidence interval for the difference in population proportions of youth who were using cosmetics in 2004 and youth who were using cosmetics in 2014. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.)

Select the correct answer below:

(−0.150,−0.070)

(−0.136,−0.084)

(−0.140,−0.080)

(−0.127,−0.093)

A certain tennis player makes a successful first serve 61​% of the time. Assume that each serve is independent of the others. If she serves 8 ​times, what's the probability she gets​ a) all 8 serves​ in? b) exactly 2 serves​ in? c) at least 6 serves​ in? d) no more than 7 serves​ in?