A sample of 52 Elementary Statistics students includes 13 women. Assuming the sample is 4. random. . . (a) Estimate the percentage of women taking Elementary Statistics with 98% confidence. (b) At 10% significance, test whether less than 40% of the enrollment in all Elementary Statistics classes consists of women. (c) If in fact 46% of the students in Elementary Statistics classes are women, find the power of the above test in detecting this parameter.

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

(e) Construct a 95% confidence interval for the population mean worth of coupons.  Use a critical value of 2.16 from the t distribution.

What is the lower bound?

(f)  Construct a 95% confidence interval for the population mean worth of coupons .

What is the upper bound? ( Round to 3 decimal places )

A major metropolitan newspaper selected a simple random sample of 544 readers from their list of 100,000 subscribers. They asked whether the paper should increase its coverage of local news, and 33% agreed that they should. What is the upper bound on the 99% confidence interval for the proportion of readers who would like more coverage of local news? Round your answer to 3 decimal places.

(THE PROBABILITIES ABOUT X) : Set up and ind the indicated probability; a diagram is recommended.

4.) The average age of a vehicle registered in the United States is 8 years, or 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles is selected, ind the probability that the mean of their age is between 90 and 100 months.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

Of 117 randomly selected adults, 35 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.

Group of answer choices

20.1% < p < 39.8%

22.9% < p < 36.9%

19.0% < p < 40.8%

21.6% < p < 38.2%

(All answers were generated using 1,000 trials and native Excel functionality.)

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

There are many products that on their label, establish a content of the packaging. Select two (2) competing brand of cleaning detergent (for example Palmolive versus Vel or Tres Monjitas versus Zuiza Dairy).

In their label, they establish a weight of the amount of detergent in each container. Choose a sample of 10 containers from the selected companies and weight the 10 samples on a scale.

Collect this information and build a hypothesis test, a confidence interval, and a P – value by comparing the average weight of the two samples.

It determines, through the hypothesis test, if there is any difference in the average weight of the two sample containers. Use an alpha for this 0.05 test.

• What is your conclusion?

An assistant in the district sales office of a national cosmetics firm obtained data on advertising expenditures and sales last year in the district’s 44 territories. Data is consmetics.csv. Use R. I don't want answers in Excel or SAS :)

X1: expenditures for point-of-sale displays in beauty salons and department stores (X$1000).

X2: expenditures for local media advertising.

X3: expenditures for prorated share of national media advertising.

Y: Sales (X$1000).

6. (4) Are there any influential points?

7. Is there a serious multicollinearity problem?

(3) Include an appropriate scatterplot and correlation values between the explanatory variables.

(3) Judge by VIF, do you think there is a problem with multicollinearity? (Hint: VIP or tolerance)

(3) Compare your answers in parts i and ii. Are your conclusions the same or different? Please explain your answer.

Data:

Below we are investigating the racial differences in occupational prestige. You will be asked to determine the area under the standard normal curve and present proportions, percentages, and counts based on that information. HINT: You’re being asked to compute z-scores and investigate their corresponding areas here. Have APPENDIX B ready!

The table below contains information on the occupational prestige scores for black and white Americans:

Mean Standard deviation N

Black Americans 40.83 13.07 195

White Americans 45.03 13.93 1,100

Use sentences to respond to the following. Please Number each of your responses, show your work for all computations, and underline your final answers. Calculate and report your answers with two decimal points unless your answers come directly from APPENDIX B.

What proportion of white Americans have an occupational prestige score above (greater than) 60? How would you write this as a percentage? Approximately how many people is this in the sample? (7.5 Points)

What proportion of black Americans have an occupational prestige score below (less than) 60? How would you write this as a percentage? Approximately how many people is this in the sample? (7.5 Points)

What proportion of white Americans occupational have an occupational prestige score between 30 and 70? How would you write this as a percentage? Approximately how many people is this in the sample? (7.5 Points)

What proportion of black Americans occupational have an occupational prestige score between 30 and 70? How would you write this as a percentage? Approximately how many people is this in the sample? (7.5 Points)

To see for yourself how the central limit theorem works, let's say we have a normal distribution (with mean =100 and standard devation = 20). Let's generate some random samples of various sizes from this distribution. We can do this in excel using =norm.inv(rand(),100,20) and it will randomly generate numbers from this distribution. I generated four samples of size 5, 10, 20 and 30, and got the means of 124 (n=5); 91 (n=10); 105 (n=20); 103 (n=30). If I continue to increase the sample size, my average values should converge to the mean of 100. Now you try. Pick a distribution and generate some sample sizes to prove this to yourself. Post and discuss your results.

An assistant in the district sales office of a national cosmetics firm obtained data on advertising expenditures and sales last year in the district’s 44 territories.

X1: expenditures for point-of-sale displays in beauty salons and department stores (X$1000).

X2: expenditures for local media advertising.

X3: expenditures for prorated share of national media advertising.

Y: Sales (X$1000).

1. Test the regression relation between sales and the three predictor variables. State the hypotheses, test statistic and degrees of freedom, the p-value, the conclusion in words.

2. Determine whether the linear regression model is appropriate by using the “usual” plots (scatterplot, residual plots, histogram/QQ plot). Explain in detail whether or not each assumption appears to be substantially violated.

For each of the examples below, draw (or describe drawing) a sampling distribution around the reported mean, mark the upper and lower limits of the 95% confidence interval, and compute the mean values that correspond to those upper and lower limits.

1. Dr. Grimm collected a random sample of 30 sociology majors and administered an IQ test (σ = 15). This group had an average IQ of M = 105. Compute a 95% confidence interval to determine the population mean of psychology majors’ IQ scores.

2. According to 2016 data from the Centers for Disease Control and Prevention, the average life expectancy in the United States is 78.6 years, with an approximate standard deviation, σ, of 15 years. A random sample of 45 dead rock musicians finds an average age of death of 45.2 years. Calculate a 95% confidence interval to determine the population mean of a rock musician’s life expectancy.

3. Dr. Morris collects information on text messaging from a random sample of 50 adults ages 25 to 44. Dr. Morris finds that these individuals send or receive an average of 75 text messages per day. Using a standard deviation, σ, of 22, calculate the 95% confidence interval for the average number of texts sent by adults in this age group.

A random sample of ? measurements was selected from a population with standard deviation ?=16.6 and unknown mean ?. Calculate a 90 % confidence interval for ? for each of the following situations: (a) ?=65, ?⎯⎯⎯=86.1 (b) ?=80, ?⎯⎯⎯=86.1 (c) ?=100, ?⎯⎯⎯=86.1

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.272.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 1.052.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²

H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    

H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²

H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent normal distributions.

The populations follow independent normal distributions. We have random samples from each population.    

The populations follow independent chi-square distributions. We have random samples from each population.

The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.200

0.100 < p-value < 0.200    

0.050 < p-value < 0.100

0.020 < p-value < 0.050

0.002 < p-value < 0.020

p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.

Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.    

Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.

Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

1.) A recent study indicated that 85% of all parents take candy from their child's trick-or-treat bag. If 30 parents are selected at random then what is the probability that 25 of them took Halloween candy from their child's trick-or-treat bag? Give your answer to four decimal places.

2.) Systolic blood pressure readings for females are normally distributed with a mean of 125 and a standard deviation of 10.34. If 60 females are randomly selected then find the probability that their mean systolic blood pressure is between 122 and 126. Give your answer to four decimal places.

3.) Apartment rental prices in Pittsburgh are approximately normally distributed with a mean of $838 and a standard deviation of $175. If a researcher wants to study people whose rent is in the lower 5% then find the maximum rent a person can pay and be part of the study. Give your answer to two decimal places and do not give units.