According to the National Eye Institute, 8% of men are red-green colorblind. A sample of 125 men is gathered from a particular subpopulation, and 13 men in this sample are colorblind.

a. Is this statistically significant evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05?

b. What is the maximum number of men that could have been colorblind in this sample that would lead you to fail to reject the null hypothesis?

c. Using 8% as the probability of being colorblind, find a 95% confidence interval for the number of men in a sample of 125 who are colorblind.

Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed, some of the cases are reversed. Kristen DelGuzzi of the Cincinnati Enquirer conducted a study of the cases handled by Hamilton County judges over a three-year period. Shown in Table below are the result for cases handled (disposed) by 4 judges in Domestic Relations Court. The purpose of the newspaper’s study was to evaluate the performance of the judges. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which judges were doing a good job and which were making too many mistakes. You have been called in to assist in the data analysis. Use your knowledge of probability and conditional probability to help with the ranking of the judges. Prepare a report with your rankings of the judges. Also, include an analysis of the likelihood of appeal and case reversal in the court. At a minimum, your report should include the following:

The probability of reversal given an appeal for each judge.

Rank the judges. State the criteria you used and provide a rationale for your choice.

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.2198.21degrees°F

and a standard deviation of

0.540.54degrees°F.

Using the empirical​ rule, find each approximate percentage below.

Concepts of convergent evidence for validity, discriminant evidence for validity, test content validity and face validity for designing a psychological test to measure happiness.

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 144 152 167 176 187 182 183 187 182 167 182 164 152 142

5. 6) I am interested in the amount of $ my friends win or lose while playing blackjack at the casinos. So I go out and collect a sample of data an obtain the following distribution of data (negative numbers mean $ was lost)
   -13, -12, -8, -4, -3, 0, 2, 4, 6, 8, 12,14

   1. What is the Range? (2pts)

   2. What is the Mean? (3pts)

   3. What is the Median? (3pts)

   4. What is the standard deviation of your sample ‘s’ (6pts)

   5. Sketch an informative error-bar chart showing the mean with error

      bars showing one standard deviation away from the mean (5pts)

   6. What are the two Quartiles (3pts)

   7. What is the 5-number summary? (3pts)

   8. What is the Interquartile Range? (3pts)

6. According to the 1.5*IQR rule, are there any potential outliers? (10pts)

7. Sketch an informative Box Plot of the distribution. (5pts)

1. A science teacher claims that the mean scores on a science assessment test for fourth grade boys and girls are equal. The mean score for 63 randomly selected boys is 151 with a standard deviation of 36, and the mean score for 65 randomly selected girls is 149 with a standard deviation of 34. At α = 0.10, can you reject the teacher’s claim? Assume the populations are normally distributed and the population variances are equal.
   Resource: Two Samples, Means, sigma known
2. In a random sample of 1216 U.S. adults, 966 favor using mandatory testing to assess how well schools are educating students. In another random sample of 1202 U.S. adults taken 9 years ago, 893 favored using mandatory testing to assess how well schools are educating students. At α = 0.05, can you support the claim that the proportion of U.S. adults who favor mandatory testing to assess how well schools are educating students is more than it was 9 years ago?

   Resource: Two Samples, Proportions

A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below.

4 4 5 5 5 5 5 6 6 6 6 12 6 6 6 7 6 7 8 7

Find the correct lower control limit

In a survey of women in a certain country​ (ages 20minus​29), the mean height was 64.9 inches with a standard deviation of 2.81 inches. Answer the following questions about the specified normal distribution. ​(a) What height represents the 95th ​percentile? ​(b) What height represents the first​ quartile? ​(a) The height that represents the 95th percentile is nothing inches. ​(Round to two decimal places as​ needed.) ​(b) The height that represents the first quartile is nothing inches. ​(Round to two decimal places as​ needed.)

2. Three randomly selected households are surveyed. The numbers of people in the households are 1​, 4​, and 10. Assume that samples of size n=2 are randomly selected with replacement from the population of 1​, 4​, and 10. Listed below are the nine different samples. Complete parts​ (a) through​ (c).

Sample            x1        x2

1          1          1

2          1          4

3          1          10

4          4          1

5          4          4

6          4          10

7          10        1

8          10        4

9          10        10

a. Find the variance of each of the nine​ samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values

                                    S^2                                                                      Probability

​(Type an integer or a fraction. Use ascending order of the sample​ variances.)

b. Compare the population variance to the mean of the sample variances. Choose the correct answer below.

A. The population variance is equal to the mean of the sample variances.

B. The population variance is equal to the square of the mean of the sample variances.

C. The population variance is equal to the square root of the mean of the sample variances.

c. Do the sample variances target the value of the population​ variance? In​ general, do sample variances make good estimators of population​ variances? Why or why​ not?

A. The sample variances do not target the population​ variance, therefore, sample variances make good estimators of population variances.

B. The sample variances do not target the population​ variance, therefore, sample variances do not make good estimators of population variances.

C. The sample variances target the population​ variances, therefore, sample variances make good estimators of population variances.

D. The sample variances target the population​ variance, therefore, sample variances do not make good estimators of population variances.

For the data set shown below, complete parts (a) through (d) below. x y 20 102 30 95 40 91 50 81 60 68 ​(a) Use technology to find the estimates of beta 0 and beta 1. beta 0 ~ b 0=_____​(Round to two decimal places as​ needed.) beta 1 ~ b 1=_____(Round to two decimal places as​ needed.) (b) Use technology to compute the standard error, the point estimate for o' (o with a little tag on the top) S e =_____(Round to four decimal places as needed.) (c) Assuming the residuals are normally distributed, use technology to determine Sb1 Sb1 =_____ (Round to four decimal places as required) (d) Assuming the residuals are normally distributed, test H0: B1 =0 versus H1:B1 =/ at the a = 0.005 level of significance. Use the P - value approach. The P - value for this test is _____ (Round to three decimal places as needed.

A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

In a random sample of 60 voters, 34 reported they voted for Candidate A and 26 reported they voted for Candidate B. Let G denote a random variable equal 1 if the person voted for A and 0 if the person voted for B.

(a) Find the sample average, ¯ G, and sample variance, S^2 G, of variable G.
(b) Does Candidate A have more than 50% of the popular vote? Formulate and test the corresponding null and alternative hypotheses to answer this question, interpret results.

(c) Are Candidates A and B virtually tied? Formulate and test the corresponding null and alternative hypotheses to answer this questions, interpret results.

A child psychologist wishes to estimate the percentage of fathers who watch their preschool-aged child when the mother works. What size sample should be obtained if she whises the estimate to be within 3 percentage points with 97% confidence if

A. she uses a 2005 estimate of 82% obtained from the U.S Census Bureau?

Z= n=

B. She does not use any prior estimates.

n=