Describe and differentiate between internal and external threats to validity in an experimental design. Recommend at least one action that you or any researcher can take in response to both internal and external validity threats.

Ms.Watts is a fan of college football, and is a little bummed the Texas Longhorns haven’t been doing as well these past few years. She has a hunch that because The Longhorns are in the highest collegiate athletic division (Division-I), her team is more likely to play a mismatched opponent. That is, The Longhorns are more likely to play games with different point spreads (winning team’s score minus losing team’s score) compared to other Divisions. To test this idea, she looked at a sample of 4 games from a lower division (Division-II) to see if the mean point spread was different compared to The Longhorns’ Division-I group. Overall, Division-I teams had a mean spread of 16.189 points with a standard deviation of 12.128 points.

1. The results of the four Division-II games from Ms. Watt's sample are below. Calculate the mean point spread for this sample.

2. Calculate the standard error.

3. State the null hypothesis based on what Ms.Watts believes about mean point spreads in Division-I compared to Division-II football games.

4. State the research hypothesis based on what Ms.Watts believes about mean point spreads in Division-I compared to Division-II football games.

5. Calculate the z-statistic to test the hypothesis you formulated in Questions 3 & 4 using the mean point spread for Division I as the comparison population to the mean point spread you calculated for #1.

6. Given the convention of p<.05, what can you conclude about the mean point spread found in Division-II compared to the mean point spread in Division-I teams? First, make a decision regarding your hypothesis, then state your conclusion.

The USA has been invaded by a ship of 6 aliens -- well, sort of, they actually just flew here from planet YB54D (known to them simply as "Home") as a part of their search for extraterrestrial life. Our military contained them immediately and we are holding them captive for further study (from this sample of 6 aliens we hope to be able to predict what the rest of their kind -- i.e., their entire population -- will be like). One of the first things we want to assess is their hostility; thus, we send in a psychologist who administers the Buss-Perry Aggression Questionnaire (BPAQ), which rates hostility on a scale of 8 to 40, with higher ratings indicating higher hostility. Their scores are as follows:

Alien 1: 20   Alien 4: 9

Alien 2: 17 Alien 5: 13  

Alien 3: 31 Alien 4: 38  

What would the BPAQ score be of an alien who is 1.5 standard deviations below the mean (round to two decimal places)?

What would the BPAQ score be of an alien who is 1 standard deviation above the mean (round to two decimals)?

1. Dihybrid crosses involving plants with either white or yellow flower and either tall or short morphs were done. The yellow allele is dominant over the white allele, and the tall allele is dominant over the short allele. The following are the observed numbers of each combination. Do these data fit the expected distribution?

a. what kind of statistical test needs to be performed?

b. Will you need to test for equal variance? If so, what are your results and how does that influence the next steps in your analysis?

c.What are your null and alternative hypotheses?

H0:

HA:

d. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

In the EAI sampling problem, the population mean is $51,900 and the population standard deviation is $4,000. When the sample size is n = 30, there is a 0.5887 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

What is the probability that the sample mean is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)?

What is the probability that the sample mean is within $600 of the population mean if a sample of size 120 is used (to 4 decimals)?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 49 ounces and a standard deviation of 7 ounces. Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.

a) 68% of the widget weights lie between ___ and ____

b) What percentage of the widget weights lie between 28 and 56 ounces?  %

c) What percentage of the widget weights lie above 35 ?  %

A sociologist surveys 50 randomly selected citizens in each of two countries to compare the mean number of hours of volunteer work done by adults in each. Among the 50 inhabitants of Lilliput, the mean hours of volunteer work per year was 52, with standard deviation 11.8. Among the 50 inhabitants of Blefuscu, the mean number of hours of volunteer work per year was 37, with standard deviation 7.2.

1. Construct the 99% confidence interval for the difference in mean number of hours volunteered by all residents of Lilliput and the mean number of hours volunteered by all residents of Blefuscu.

2. Test, at the 1% level of significance, the claim that the mean number of hours volunteered by all residents of Lilliput is more than ten hours greater than the mean number of hours volunteered by all residents of Blefuscu.

3. Compute the observed significance of the test in part (b).

What are the criteria used for evaluating a discrimination funtion? define them.

Now that you have a better idea about what differentiates a one sample chi square from an independent samples (two factor) chi square, I want you to come up with one study idea that would use a one sample chi square and one study that would use an independent samples (two factor) chi square.

A circle of radius r has area A = πr2. If a random circle has a radius that is uniformly distributed on the interval (0, 1), what are the mean and variance of the area of the circle?

Change the distribution of the radius to an exponential distribution with paramter β = 2. Also find the probability that the area of the circle exceeds 3, if it is known that the area exceeds 2.

An online shoe retailer sells women’s shoes in sizes 5 to 10. In the past orders for the different shoe sizes have followed the distribution given in the table provided. The management believes that recent marketing efforts may have expanded their customer base and, as a result, there may be a shift in the size distribution for future orders. To have a better understanding of its future sales, the shoe seller examined 1,174 sales records of recent orders and noted the sizes of the shoes ordered. The results are given in the table provided. Test, at the 1% level of significance, whether there is sufficient evidence in the data to conclude that the shoe size distribution of future sales will differ from the historic one.

Use the data below to answer the questions in this assignment.

You will first need to enter the following data in SPSS with “age” and “hours” as your variable names.

Age and Hours on Computer Data

Age (X): 24, 23, 23,25,27, 21,21,30,21,29

Number of hours on spent on computer per week (Y): 14,24,18,23,19,23,16,10,6,15

This question is only being used to describe the data set. In the box below you only need to enter 0.

Run a correlation analysis in SPSS to test whether or not there is a relationship between age and hours.

Statistical Significance:

Based on your SPSS results, state the specific probability that the r coefficient (i.e., correlation) value found was due to error and comment on whether or not your results are statistically significant.

Practical Significance:

Based on your SPSS results, state the value of the effect size and comment on whether the effect is practically significant.

We have learned hypothesis tests

1. for the mean (when population variance is known and when it is unknown)
2. for a percentage
3. to see if the means of two sets of data are the same
4. goodness of fit test
5. test for independence

For each type give a brief example. You do not have to solve the problem you give.

A random sample of 400 electronic components manufactured by a certain process are tested, and 30 are found to be defective.

a) Let p represent the proportion of components manufactured by this process that are defective. Find a 95% confidence interval for p. Round the answers to four decimal places.

b) How many components must be sampled so that the 95% confidence interval will specify the proportion defective to within ±0.02? Round up the answer to the nearest integer.

c) The company ships the components in lots of 200. Lots containing more than 20 defective components may be returned. Find a 95% confidence interval for the proportion of lots that will be returned. Use the normal approximation to compute this proportion. Round the answers to four decimal places.