Consider sampling heights from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is μ = 67 inches and the standard deviation is σ =3.6 inches.

Suppose we randomly sample 98 values from this population and compute the mean, then repeat this sampling process 5000 times and record all the means we get.

Which of the following is the best approximation for the mean of our 5000 sample means?

1. 6.8
2. 98
3. 67

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 52.0 kg and standard deviation σ = 9.0 kg. Suppose a doe that weighs less than 43 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 49 kg. If the average weight is less than 49 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 70 does is less than 49 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 53.6 kg for 70 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was

x

= 53.6 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.Since the sample average is above the mean, it is quite likely that the doe population is undernourished.    Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

The number of letters handled daily by a post office is normally distributed with a mean of 20,000 letters and a standard deviation of 100 letters. Find the percent of days on which the post office handles:

A.) more than 20,200 letters

B.) fewer than 19,900 letters

C.) Between 19,950 and 20,050 letters

D.) between 20,100 and 20,150 letters

A researcher hypothesizes that the percentage of Ball State University students who sleep 8 or more hours per night is lower than the general population of adults. Previous research has found that 40% of adults sleep 8 hours or more per night. In a recent survey of Ball State students, the researcher found that 38 students reported sleeping 8 hours or more and 82 students reported sleeping less than 8 hours. Do the Ball State student sleep habits differ from those expected of the general population of adults?

a. Using Excel, conduct a Chi-square goodness of fit test on these data.

b. Report the results in a textbox. Be sure to provide both a statistical and research conclusion.

You collect data to answer the research question, “Are high school boys involved in more automobile accidents than high school girls?” After conducting a hypothesis test, you conclude that there is sufficient evidence to reject the null hypothesis at α = 0.05. Use complete sentences to answer the following.

a. What were your null and alternative hypotheses in words?

b. State your conclusion pertaining to real-life in words.

c. If this conclusion is actually NOT correct, what type of error is this? State the correct conclusion in words.

d. What are some possible consequences of this error?

e. How might you change the alpha level to reduce this type of error? Explain.

The capacities (in ampere-hours) were measured for a sample of 120 batteries. The average was 178 and the standard deviation was 12.

a.)

Find a 95% lower confidence bound for the mean capacity of this type of battery. Round the answer to two decimal places.

b.) An engineer claims that the mean capacity is greater than 175 ampere-hours. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.

1. What is the purpose of cross-validation? Specifically, why wouldn’t we test a hypothesis trained on all of the available examples?

Eight male and eight female college students who have credit cards were surveyed and asked their total credit card debt. The responses are given below in dollars:

1. Is this an observational study or a designed experiment? Explain your answer.

2. Is it reasonable to use Welch’s t-test? Explain your answer.

3. Is there a difference in the mean credit card debt of males and females? Use α = 0.10. List out all 5 steps in the hypothesis testing and show your work.

Step 1

Step 2

Step 3

Step 4

Step 5

4. Construct a 90% confidence interval for the difference in the mean credit card debt of male and female college students.

Lower Bound:    

Upper Bound:  

Choose a study design and justify the reasons you chose the design over others.

Select a statistical measure you would use to describe the association (if there is one) between body mass index and asthma.

In addition, address: Subject selection Issues relating to the measurement of both the exposure and the outcome Potential biases that the study might be prone to, and how they might be handled Possible confounding factors and effect modifiers and how to overcome their effect

Kindly explain your copy paste. Thanks.

Riehl (1994) examined whether Indiana University students who were the first generation in their family to attend college were more at risk of dropping out during their first semester than other students. The table below shows the observed frequencies:

a. Using Excel, conduct a Chi-square test of independence on these data.

b. Report the results in a textbox. Be sure to provide both a statistical and research conclusion.

What are three different techniques a researcher can use to establish convergent validity of a measure? Explanation and examples please!

-Research Methods and Statistics

A researcher would like to evaluate the effectiveness of a pain-relief patch designed for lower back pain. Prior to testing the patch, each of n = 4 patients rates the current level of back pain on a scale from 1 to 8. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows.

​

                                                Before        After

                                          __________________

                   G = 36                  6          2

                  G² = 784                6          2

                ΣX² = 192                4          4

                                                8          4

                                         ______________________

                                            T = 24   T = 12

                                          SS = 8    SS = 4

Perform an ANOVA and then analyze the data with a t-test. Use the .05 level of significance for both.

An independently selected sample of five men also participated in the same study. The table below shows results for the number of pounds lost by the five men and the five women in the study. The researcher will use the .01 significance level to test whether (on average) the program produces different weight loss results for men and women. You may assume the population variances are equal (although the sample variances are not).

f. Formulate the hypothesis for this test.

g. Should the pooled-sample variance be used in this situation? Why?

h. Choose the appropriate formula for the test statistic and find its value.

i. What is the rejection region for this test?

j. What should the researcher conclude?

St. Andrew’s University receives 900 applications annually from prospective students. The application forms contain a variety of information including the individual’s scholastic aptitude test (SAT) score and whether or not the individual desires on-campus

housing.

What is the probability that a simple random sample of 30 applicants will provide an estimate of the population mean SAT score that is within plus or minus 10 (within 10 points) of the actual population mean m ? Given that the population Standard Deviation is 80.

Data show 648 applicants wanting On-Campus Housing. What is the probability that sample proportion exceeds 50%, when n =30?

What is the probability that a simple random sample of 30 applicants will provide an estimate of the population proportion of applicants desiring on-campus housing that is within plus or minus .05 of the actual population proportion?

If the University can provide to no more than 45% for the on –campus housing facilities, what would be the estimated number of accepted applicants desiring on-campus housing?

4. Suppose a company wants to find the determinants of job satisfaction for its employees. The company gathers some anonymous data from its employees and runs a regression with Job Satisfaction (on a 1 to 10 scale) as the response variable, and it gets the following results.

ANOVA

(a) What are the null and alternative hypotheses (regarding the b values) for the F-test for the regression?

(b) What is the F-statistic for this regression

(c) The critical F* for the test is 5.04. Do we reject or not reject the null hypothesis in this case?

Why?

(d) What percentage of the variation in Job Satisfaction is “explained” by this regression?