3. What does the test statistic tell us?

4. Why do we divide by the standard error when computing a test statistic?

5. Why do we reject the null hypothesis when the p-value is small? Explain as if to someone unfamiliar with

statistics.

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 78 cars owned by students had an average age of 5.04 years. A sample of 118 cars owned by faculty had an average age of 8 years. Assume that the population standard deviation for cars owned by students is 3.06 years, while the population standard deviation for cars owned by faculty is 3.24 years. Determine the 98% confidence interval for the difference between the true mean ages for cars owned by students and faculty.

Step 3 of 3: Construct the 98% confidence interval. Round your answers to two decimal places.

Month Jan-12 Feb-12 Mar-12 Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12

Profit ($) 5,700 5,453 5,034 4,717 5,185 5,638 6,519 6,182 5,913

Step 2 of 5: What are the MAD, MSE and MAPE scores for the three-period moving average? Round any intermediate calculations, if necessary, to no less than six decimal places, and round your final answer to one decimal place.

Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.02 significance level.

The null and alternative hypothesis would be:

H0:μM=μFH0:μM=μF
H1:μM≠μFH1:μM≠μF

H0:pM=pFH0:pM=pF
H1:pM≠pFH1:pM≠pF

H0:pM=pFH0:pM=pF
H1:pM<pFH1:pM<pF

H0:μM=μFH0:μM=μF
H1:μM<μFH1:μM<μF

H0:μM=μFH0:μM=μF
H1:μM>μFH1:μM>μF

H0:pM=pFH0:pM=pF
H1:pM>pFH1:pM>pF

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 60 men, 45% owned cats
Based on a sample of 60 women, 60% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Explain how you can use difference in difference to identify causal identification in a research paper

Let's consider an urn that contains 15 balls, of which 5 are black balls. An integer n is randomly selected from the set {1, 2, 3, 4, 5, 6, 7, 87}, and then a sample of size n is obtained without replacement of the urn. Find the probability that all the balls in the sample are black.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 16 engines and the mean pressure was 8.2 pounds/square inch with a standard deviation of 0.5. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

• Fit a simple linear regression model to each set of (x, y) data, i.e., one model fit to (x₁, y₁), one model fit to (x₂, y₂), one model fit to (x₃, y₃), and one model fit to (x₄, y₄).

• Write down the estimated regression equation for each fitted model, together with the values of the coefficient of determination, r2, and the standard error of the estimate, s=MSE‾‾‾‾‾√.

• For each set of (x, y) data, create a scatterplot of y (vertical) versus x (horizontal) with the estimated regression line added to the plot.

• For each set of (x, y) data, create a scatterplot of the residuals (vertical) versus (horizontal). Based on each plot, do the zero mean and constant variance assumptions about the simple linear regression model error seem reasonable?

• For each set of (x, y) data, create a normal probability plot of the standardized residuals. Based on each plot, does the normality assumption about the simple linear regression model error seem reasonable?

• For each set of (x, y) data, are there any outliers?

• For each set of (x, y) data, are there any high leverage points?

• For each set of (x, y) data, are there any influential points?

  Post a summary of your group’s analysis. What important “big picture” conclusions can you draw from your analysis?

A car company advertises that their Super Spiffy Sedan averages 29 mpg (miles per gallon). You randomly select a sample of Super Spiffies from local dealerships and test their gas mileage under similar conditions.

You get the following MPG scores:

33 27 32 34 34 28 27 31

Note: SSx = 63.50

Using alpha =.01, conduct the 8 steps to hypothesis testing to determine whether the actual gas mileage for these cars differs significantly from 29mpg.

During a blood-donor program conducted during finals week for college students, a blood-pressure reading is taken first, revealing that out of 300 donors, 44 have hypertension. All answers to three places after the decimal.

The probability, at 60% confidence, that a given college donor will have hypertension during finals week is? , with a margin of error of?

Assuming our sample of donors is among the most typical half of such samples, the true proportion of college students with hypertension during finals week is between?. and?

We are 99% confident that the true proportion of college students with hypertension during finals week is ? , with a margin of error of ?. .

Assuming our sample of donors is among the most typical 99.9% of such samples, the true proportion of college students with hypertension during finals week is between ? and ?

Covering the worst-case scenario, how many donors must we examine in order to be 95% confident that we have the margin of error as small as 0.01? Using a prior estimate of 15% of college-age students having hypertension, how many donors must we examine in order to be 99% confident that we have the margin of error as small as 0.01? .

Suppose that ?!,···, ?" form a random sample from the beta distribution with parameters ? and
?. Find the moments estimators for ? and ?.

NOTE: Please make the solution as well detailed as possible especially the making of ? and
? the subject of formular respectively

Thalidomide is a tranquilizer that was prescribed in the late 1950’s and early 1960’s to pregnant women, with the devastating result of over 12,000 birth defects in 48 countries before it was banned in 1962. (It was never sold in the United States.) Since then, the drug has reappeared as a possible solution to a number of medical problems. The U.S. National Institutes of Health announced on 31 October 1995 the results of a study in 30 hospitals of the effectiveness of thalidomide in healing mouth ulcers in AIDS patients. In the study, which was chaired by Dr. Jeffrey Jacobson of the Bronx Veteran Affairs Medical Center and the Mount Sinai School of Medicine in New York, it was found that 14 out of 23 patients who received thalidomide had their ulcers heal compared to 1 out of 22 patients who received a placebo. As a result of these early trial outcomes, the researchers suspended the trial giving thalidomide to all the patients in the study. THIS IS ALL THE INFO GIVEN.

1. Find a 90% confidence interval for the difference in proportion of healing assuming that both samples are simple random samples and independent of each other.
2. Conduct the appropriate large-sample test of significance. Discuss your results and compare your conclusion with the decision of the researchers.
3. By hand, draw a bar graph depicting the sample proportions of healing. Add a whisker to the top of each bar to denote the standard error of the sample proportion.  DO NOT SUBMIT.
4. Examine the bar graph you produced for part (a). Briefly comment on whether there appears to be a difference in proportions.
5. Conduct the appropriate hypothesis test for a two-by-two contingency table and report the P-values for Fisher’s exact test and the asymptotic chi-square distribution approximation for this test. Compare these results with your answer to part (b) in Exercise 1.

The following data represent the concentration of dissolved organic carbon​ (mg/L) collected from 20 samples of organic soil. Assume that the population is normally distributed. Find sample mean, standard deviation and construct a 99% confidence interval the population mean m.

5.20 29.80 27.10 16.51 14.00

8.81 15.42 20.46 14.90 33.67

30.91 14.86 7.40 15.35 9.72

19.80 14.86 8.09 14.00 18.30

What is the difference between statistical and economic significance? Give an example. (Your own example, NOT a pill for cancer).

QUESTION ONE

You want to find out the performance of county XYZ and you have been given the following   secondary data in tabular form of the country’s Gross Domestic Product (GDP in K’m), broken down into three different categories, for three separate years.

Present, illustrate, interpret and analyse the information using a) A Pictogram

2. A bar chart
3. A compound (multiple) bar chart
4. A component bar chart

The GDP for 2018 using a pie chart