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.

Background: This activity is based on the results of a recent study on the safety of airplane drinking water that was conducted by the U.S. Environmental Protection Agency (EPA). A study found that out of a random sample of 316 airplanes tested, 40 had coliform bacteria in the drinking water drawn from restrooms and kitchens. As a benchmark comparison, in 2003 the EPA found that about 3.5% of the U.S. population have coliform bacteria-infected drinking water. The question of interest is whether, based on the results of this study, we can conclude that drinking water on airplanes is more contaminated than drinking water in general.

Question 1: (Remember write all answer in an MS Word doc and upload)

Let p be the proportion of contaminated drinking water in airplanes. Write down the appropriate null and alternative hypotheses.

Question 2:

Based on the collected data, is it safe to use the z-test for p in this scenario? Explain.

Use the following instructions to conduct the z-test for the population proportion:

Instructions - 2 Options

Option 1: Click on the following link to use the MS Excel hypothesis test template: hypothesis.xls
R | StatCrunch | Minitab | Excel 2007 | TI Calculator

Question 3:

Now that we have established that it is safe to use the Z-test for p for our problem, go ahead and carry out the test. Paste the output below.

Question 4:

What is the test statistic for this test? (Hint: Calculation already done by either technology option.) Interpret this value.

Question 5:

What is the P-Value? Interpret what that means, and draw your conclusions. Assume significance level of 0.05.

An animal’s maintenance caloric intake is defined as the number of calories per day required to maintain its weight at a constant value. We wish to discover whether the median maintenance caloric intake, m, for a population of rats is less than 10g/day. We draw a SRS of 17 rats, feed each rat 10g of dry food per day for30 days, and find that 4 of the rats lost weight, while the rest gained weight.

(a) State null and alternative hypotheses in terms of m.

(b) Let B be the number of rats in a SRS of size 17 that exhibit daily caloric demands more than 10g/day.IfH0is true, what is the distribution ofB?

(c) What is the value of B observed in the study?

(d) Use the sign test to calculate the p-value and draw a conclusion using α= 0.05.

In a time-use study, 20 randomly selected college students were found to spend a mean of 1.4 hours on the internet each day. The standard deviation of the 20 scores was 1.3 hours.
Construct a 90% confidence interval for the mean time spent on the internet by college students. Assume t* = 1.729
If you increased the sample size for the problem above, what would happen to your confidence interval, assuming the sample mean and standard deviation remain unchanged?

A study is conducted regarding shatterproof glass used in automobiles. Twenty-six glass panes are coated with an anti-shattering film. Then a 5-pound metal ball is fired at 70mph at each pane. Five of the panes shatter. We wish to determine whether, in the population of all such panes, the probability the glass shatters under these conditions is different from π= 0.2

(a) State the appropriate null and alternative hypotheses.

(b) Check the conditions for trusting the conclusion of the test, and calculate the observed value of an appropriate test statistic.

(c) Calculate the rejection region and draw a conclusion, given the significance level α= 0.05.

(d) Calculate the p-value.

(e) Compute the power of the test if the trueπwas in fact 0.3.

W72A) I am learning EXCEL Functions. Please answer in EXCEL Functions in detail

Stock Returns (relationship between hypothesis testing and confidence intervals)

Suppose you as an investor with a stock portfolio of hundreds of thousands of dollars decide to sue your broker because of low returns due to lack of portfolio diversification, i.e., too many holdings with similar return prospects. The 39 monthly returns, expressed as percentages, are shown in the table below and reproduced in your Excel answer template.

If we graph these data in a histogram, we can reasonably infer that the data are distributed normally.

Suppose you’re on an arbitration panel reviewing this case and decide to compare these returns with the Standard & Poor’s (S&P’s) stock index over the same period and find that the S&P mean, which we can interpret as the population mean (μ), equals .95%.

1.        Test (two-sided) at the 5% level that the mean return you compute   from the investor’s 39-month sample differs from the S&P (population) mean. Use the P-value method, rounding to 4 digits. Make sure to state the null and alternate hypotheses, claim, and your conclusion.   

Remember: since we must compute the sample standard deviation, use the t-statistic to perform the test.)

2.       Now use your P-value calculated in (a) to test at the 1% level whether the sample mean differs from the S&P population main, making sure to state your conclusion. (Do not restate the hypotheses. Simply state the conclusion.

3.        Compute a 95% confidence interval for the population mean,

using the data given in the Table above for α = .05. (Express the results with three decimal places, one more than given in the data.) Does the S&P mean lie in the interval you’ve computed?

4.        Now compute a 99% confidence interval for the population mean, expressing the results with three decimal places. Does the S&P mean lie in the interval you’ve computed?