# Statistics problems and questions

I managed to do all my other questions but I cannot figure these specific problems out. They are not fully explained in the book and I cannot figure it out by searching for help online. I have worked all day yesterday and most of today on this and just cannot get these specific problems! If you could explain how to do them with step-by-step instructions with the answers included, I would like to learn so I do not get behind in class. Thank you!

1. What are the primary advantages of a repeated-measures design over an independent-measures design?

2. The results of two repeated-measures studies are summarized as follows: The first study produces a sample with MD = 4 and s= 9, and the second study produces MD = 12 and s = 9. Assume b = 10 for both samples. In each case, the sample mean and sample standard deviation should provide enough information for you to visualize (or sketch) the sample distribution.

a. For each sample, identify where a value of zero is located. (Is zero in the middle of the sample or is it an extreme, unrepresentative value for the sample?)

b. Assuming that the samples are representative of their populations, which of the two samples is more likely to have come from a population with a mean difference of uD = 0? (Which sample is more likely to accept a null hypothesis that UD = 0?)

3. Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this phenomenon, a sample of n= 20 college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged MD= 6.3 points better on the first test, with SS for the difference scores equal to 2375.

a. Do the data demonstrate a significant change in problem-solving ability? Use a two-tailed test with x =. 05

b. Compute an estimate d to measure the size of the effect.

4. Explain why it would not be reasonable to use estimation after a hypothesis test for which the decision was fail to reject Ho.

5. A sample of n = 9 scores is obtained from an unknown population. The sample mean is M = 46 with a standard deviation of s = 6.

a. Use the sample data to make an 80 % confidence interval estimate of the unknown population mean.

b. Make a 90% confidence interval estimate of u.

c. Make a 95 % confidence interval estimate of u.

d. In general, how is the width of a confidence interval related to the percentage of confidence?

6. Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was u = 15.1. A sample of n = 16 of today's children produces a mean score of M = 23.3 with SS = 240.

a. Based on the sample, make a point estimate of the population mean anxiety score for today's children.

b. Make a 90% confidence interval estimate of today's population mean.

#### Solution Preview

Dear Student,

The answers are given below.

Best of Luck

OTA 103881

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sqrt means square root of in all the answers.

1. A repeated measures design is a longitudinal study, usually a controlled experiment but sometimes an observational study (often referred to as a longitudinal or panel study). A popular repeated-measures design is the crossover study. A crossover study is a longitudinal study in which subjects receive a sequence of different treatments (or exposures). Crossover designs are common for experiments in many scientific disciplines, for example psychology, education, pharmaceutical science, and health-care, especially medicine.

The primary strengths of the repeated measures design is that it makes an experiment more efficient and helps keep the variability low.

This design helps to keep the validity of the results higher, while still allowing for smaller than usual subject groups. This is

advantageous compared to an independent-measures design where a subject is used only once. The advantage can be important when it is hard to find subjects and leads to more economic use of subjects.

One of the main disadvantages of using independent measures design is the potential for error resulting from individual differences of the participants of each separate group, which would affect the results. This can be avoided in a repeated-measures design by using the same subjects.

2. The results of two repeated-measures studies are summarized as follows: The first study produces a sample with MD = 4 and s= 9, and the second study produces MD = 12 and s = 9. Assume b = 10 for both samples. In each case, the sample mean and sample standard deviation should provide enough information for you to visualize (or sketch) the sample distribution.

b = 10 is the sample size.

a. For each sample, identify where a value of zero is located. (Is zero in the middle of the sample or is it an extreme, unrepresentative value for the sample?)

The standard deviation of MD = s/sqrt(10) = 9/sqrt(10) = 2.846

For the first study, the scaled value for 0 = (0 - 4)/2.846 = -1.40548

For the second study, the scaled value for 0 = (0 - 12)/2.846 = -4.216

These ...

#### Solution Summary

What are the primary advantages of a repeated-measures design over an independent-measures design?

How to calculate the population mean given sample mean?

How to perform a 1 sample t test?