Bernard Haldane Associates conducted a survey in March 2004 of 1021 workers who held white-collar jobs but who had changed jobs in the previous twelve months. Of these workers, 56% of the men and 35% of the women were paid more in their new positions when they changed jobs. Suppose that these percentages are based on random samples of 510 men and 511 women white-collar workers.

1. Construct a 95% confidence interval for the difference between the two population proportions.

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2. Using the 2% significance level, can you conclude that the two population proportions are different? Use the p-value approach.

A clinic developed a diet to impact body mass (fat and muscle). A nutritionist in the clinic hypothesizes that heavier individuals on the diet will predict more body fat. Below are the data for a sample of clients from the clinic. Weight is measured in kilograms (kg) and percentage body fat is estimated through skinfold measurement. What can the nutritionist conclude with an α of 0.05?

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected a):

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

More weight of individuals on the diet significantly predicts more body fat.More weight of individuals on the diet significantly predicts less body fat.    The weight of individuals on the diet does not significantly predict body fat.

A review session is given in order to find if the group who attends it has a better average than who doesn't. The grades are organized into two independent groups and the data is obtained. The mean and standard deviation of the 29 students who attended the review session are 70.5 and 11.6 percent respectively. The mean and standard deviation of the 14 students who did NOT attend the review session are 64.6 and 16.1 percent respectively. In this problem, you will calculate the 90%, 95% and 99% confidence intervals for the difference in the mean of the two student test groups and determine if there is a true difference in the average of the two groups. We will assume for this part of the problem that we consider the variances are NOT "equal." Perform the following steps:

What is the standard error of the mean for the three confidence intervals?

What is the margin of error for each of the three confidence intervals?

Construct the 90%, 95% and 99% confidence intervals for the "true" difference between the test averages of the two groups, showing first the mean +/- the margin of error, and then showing the range of the interval.

Is there a true "difference" in the means of the review session attenders vs. those who did not? On what information provided by the confidence intervals are you basing your answer?

Suppose there are 54% female students on CMU campus. A random sample of 100 students was obtained. What is the probability there will be equal to or more than 58 female students?

How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistinguishable Republicans, indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group have a majority of the committee members?

Suppose a long jumper claims that her jump distance is less than 16 feet, on average. Several of her teammates do not believe her, so the long jumper decides to do a hypothesis test, at a 10% significance level, to persuade them. she makes 19 jumpes. The mean distance of the sample jumps is 13.2 feet. the long jumper knows from experience that the standard deviation of her jump distance is 1.5 ft

A. State the null and alternate hypothesis

B. Compute the test statistic

C. State long jupers conclusion (you can use p value or Critical value)

Simulate a distribution of 500 t-scores with 24 degrees of freedom into a variable called tsim using the rt() function. Solve using R.

A student records the repair cost for 13 randomly selected TVs. A sample mean of $72.19 and standard deviation of $15.88 are subsequently computed. Determine the 98% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal.

1) Find the critical value that should be used in constructing the confidence interval. Round you answer to three decimal places.

2) Construct the 98% confidence interval. Round your answer to two decimal places.

The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, someone who knows wh at's behind the doors (Monty Hall) opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). The Monty Hall problem is deciding whether you change your selection or not that has a better chance of winning the car . It’s common sense that if not to change, the probability of winning is 1/3 but what about changing the selection.

Simulating this game using SAS, for each round, program the fol lowing, 1) Assigning two goats and a car to three doors randomly 2) Picking a door randomly 3) Picking one of the two remaining doors to open but must showing the goat 4) Changing the selection to the remaining door 5) Deciding the result Repeating these steps for 100 round s , generating a data set including the following five variables, the round number, the door the car is in, the door chosen initially, the door chosen after switching, and the result(win/lose). Showing the data set and r eporting the frequenc y of the i nitial door chosen, the frequenc y of the door chosen at the end, the average rate of winning.

In a recent study, among recently-graduated university students of the sample, only 4% of them wrote with their left hand. Yet, among grade 1 elementary-school students from the same sample, a full 20% of them wrote with their left hand. What is wrong with the conclusion from these data that writing with the left hand is bad for university success?

In the early 1900s, Latter (1902) investigated the behavior of female cuckoos, that lay their eggs on the ground and then move them to the nests of other birds. In particular, Latter gathered data on the lengths of the cuckoo eggs found in these foster-nests. Data based on this work is used in (Tippett, 1952) and is located in the file cuckoos. The data contains the lengths, in millimeters, of the lengths of cuckoo eggs and the species of the nests where the eggs were placed. Get the data by installing and loading the resampledata R package, and use the Cuckoos dataset.

a. Create side-by-side boxplots (in R) to compare the distribution of lengths across the different foster nests.

b. Conduct an ANOVA test (also in R) to see if the mean lengths of the cuckoo eggs are the same across the different foster nests.

c. Perform the Tukey Honestly Significant Difference test (without p-value adjustment) to compare all pairwise means. What can you conclude from this analysis? d. Do the Tukey HSD test using the p-value adjustment method of your choice. Do your conclusions from “2c” change? Given the number of pairwise contrasts, without p-value adjustment, what would be your family-wise error rate if you were to conduct each pairwise contrast at /alpha = .05?

Using R, conduct an ANOVA to see if there are differences in weight between two groups of monkeys. What is null hypothesis conclusion with evidence.

Conduct a post-hoc MCP (use TukeyHSD) to see which means are different. What do the outputs lwr and upr mean?

The numbers are

monkey group 1= 9.7, 9.2, 9.5, 9.5, 10.9, 9.8, 8.7, 7.9, 9.8, 9, 10.5, 8.9, 10, 8.9, 6.8, 9.3, 8.2, 8.5, 9.4, 10.5

Monkey group 2= 8.1, 7.8, 7.6, 9.9, 8.1, 9.1, 8.8, 10.4, 8.6, 6.9, 9.1, 6.7, 7.3, 7.8, 9.6, 8.7, 5.5, 9.5, 8.2, 7.8

Please Conduct a Paired Difference Test (use α=5%) for the two data sets below. Thanks.

2012          2015

Seventy percent of adults favor some kind of government control on the prices of medicines. A random sample of 400 adults was selected to determine whether or not they favor some kind of government control.

(a) Are the conditions necessary to apply the CLT satisfied? Explain.

(b)Describe and sketch the sampling distribution of the sample proportion in this situation.

(c) Find the probability that the proportion of adults who favor some kind of government control is less than 0.65.

(d)Find the probability that the proportion is between 0.73 and 0.76.

A food company has developed a high mineral sea salt (sodium). A nurse practitioner wants to know if blood pressure can be predicted from the sodium intake of the new sea salt. Below are the sodium and BP measurements for a sample of participants that regularly use the new sea salt. What can the nurse practitioner conclude with α = 0.01?

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected a):

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

More sodium intake significantly predicts an increase in blood pressure.More sodium intake significantly predicts a decrease in blood pressure.    Sodium intake does not significantly predict blood pressure.