Statistics and Probability Answers

3. A researcher is interested in whether listening to music helps or hinders test-performance. To control for differences in cognitive level, this researcher decides to use a within-participants design. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. Participants take a 20-item quiz on the material. The table below shows the scores on the quiz. The study is completely counterbalanced to control for order effects. The scores obtained are measured on an interval-ratio scale and are normally distributed.
Music No Music
17 17
16 18
15 17
16 17
18 19
18 18

a. What statistical test should be used to analyze the data?

b. Is this a one- or two tailed test?

c. Identify H0 and Ha for this study.

d. Conduct the appropriate analysis. Should H0 be rejected? What should the researcher conclude?

e. Calculate the 95 confidence interval.

2. A teacher wants to investigate whether there is a difference between male and female students in the amount of time they spend studying for statistics. The table below shows the amount of time students spend studying statistics each week. The amounts of time spent studying are normally distributed.
Male Female
27 25
25 29
19 18
10 23
16 20
17 15
15 19
a. What statistical test should be used to analyze the data?

b. Is this a one- or two tailed test?

c. Identify H0 and Ha for this study.

d. Conduct the appropriate analysis. Should H0 be rejected?

1. An LU professor is interested in whether there is a difference between undergraduate students and graduate students in the amount of time spent praying each day. The professor gathers information from random samples of undergraduate and graduate students on the LU campus. The amount of time praying is normally distributed and is measured on an interval/ratio scale.
Graduate Undergraduate
15 9
17 11
10 9
13 6
11 5
17 6

a. What statistical test should be used to analyze the data?


b. Is this a one- or two tailed test?


c. Identify H0 and Ha for this study.


d. Conduct the appropriate analysis. Should H0 be rejected?

how many three digit numbers can be formed from the digits 1,2,3,4,and 5 if each digit can be used only once

The Independent-sample t-test

Is there any evidence that leadership style (as measured by the amount of controlling behavior) differs between principals in urban and rural areas in Oromia? Data are provided below:
Urban: 78.56 Roral: 69.60
s = 16.7 s = 19.31
n = 9 n = 10

The paired t-test

A large group of learning-disabled college freshmen, who experienced debilitating anxiety before major tests, were matched on an index of test anxiety. Members of these matched pairs were randomly assigned to two different groups. The first group was given two weeks of relaxation exercises (Relax). The second group of students was given two weeks of study skills training (Study). Using the data below determine if there is a significant difference between their final exam scores. Use this data

Relax: 46 49 47 48 50 52 48 47 46 49 42
Study (y) 50 49 51 52 50 48 52 47 50 52 53

The Independent-samples t-test

An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty years of age. The investigator administers a vocabulary test to a group of 31 younger subjects and to a group of 31 older subjects. Higher scores reflect better performance. The mean score for younger subjects was 14.0 and the standard deviation of younger subject's scores was 5.0. The mean score for older subjects was 20.0 and the standard deviation of older subject's scores was 6.0. Does this experiment provide evidence for the investigator's theory?

65 percent of homes in Canada were found to have computers. In a sample of 8 homes, what is the probability that 5 have computers?

SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
QUESTION 1
A company sells packets of biscuits that they claim, on average, contains at least 20 g biscuits in each packet. They admit that their claim is wrong (and will refund any money) if a sample of 40 has a mean less than 19.8 g. If the standard deviation is 0.5 g,
a) Formulate the appropriate null and alternative hypotheses, and determine the type of test.
b) If the test is conducted at α = 0.05, determine the critical value that specify the rejection region, then complete this sentence: Reject H¬0 if test statistic is ___________________
c) Find the probability of a Type I error.
d) Find the probability of a Type II error and determine the power of test if the true mean is 19.5 g

SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
A researcher wishes to determine whether the average amount of bleaching agent in a 1kg packet of brand X wheat flour exceeds that of brand Y. Fifteen 1kg packets of wheat flour for each brand were selected at random. It is found that on average, X contains 5% bleaching agent with a standard deviation of 0.3 and Y contains on average, 4% bleaching agent content with standard deviation of 0.5.
a) Obtain the point estimate of the mean difference of the bleaching agent content in a packet of 1kg wheat flour.
b) Determine the sampling distribution for the mean difference of the bleaching agent in a 1kg packet of wheat flour.
c) Formulate the appropriate null and alternative hypotheses to be tested.
d) Calculate the test statistics for the test.
e) Interpret your findings at 5% level of significance.