Textbook #1: Lane et al. Introduction to Statistics, David M. Lane et al., 2013.
( http://onlinestatbook.com/Online_Statistics_Education.pdf )
Textbook #2:Illowsky et al. Introductory Statistics, Barbara Illowsky et al., 2013.
( http://openstaxcollege.org/files/textbook_version/hi_res_pdf/15/col11562op.pdf )
See the file named “UMUC_STAT200_EXCEL_Tips” at the “Course Materials” menu link to find functions for calculating the Normal Distribution and Student’s Tdistribution values needed for this assignment.
Lane – Chapter 11: (18)
18. You choose an alpha level of .01 and then analyze your data.
a. What is the probability that you will make a Type I error given that the null hypothesis is true?
b. What is the probability that you will make a Type I error given that the null hypothesis is false?
Lane – Chapter 12: (7,13)
7. Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data in the table below.
a. Compute L (linear effect of trial) for each subject using the contrast weights 1, 0, and 1. That is, compute (1)(a) + (0)(b) + (1)(c) for each subject. Make a new column in your table with this result.
b. Compute a onesample ttest on this column (with the L values for each subject) you created.
HINT: See the example in the “Specific Comparisons” section of Chapter12. Find the “tvalue” and the “twotailed probability” using the EXCEL “TDIST” function. Assume the statistic for this problem is “L” and use the following formula for the tvalue. Also assume the hypothesized value is 0, since the contrast weighting (1,0,+1) for a “perfect” set of data would make “L” be 0 in all cases.
t = (statistic – hypothesized value) / (standard error of the statistic)
t = (Mean of L – 0) / (Standard Error of L)
tvalue =
X = Sample Mean
S = Sample Standard Deviation
N = Number of LSamples
13. You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The first group had a mean score of 75 and a variance of 120. The second group had a mean score of 86 and a variance of 100.
HINT: See Chapter12 section on “Differences between two means (independent groups)”.
a. What is the calculated t value? Are the mean test scores of these two groups significantly different at the .05 level?
b. What would the t value be if there were only 6 participants in each group? Would the scores be significant at the .05 level?
Lane – Chapter 13: (4)
4. Rank order the following in terms of power.

Population1 Mean 
n 
Population2 Mean 
Standard Deviation 
A 
29 
20 
43 
12 
B 
34 
15 
40 
6 
C 
105 
24 
50 
27 
D 
170 
2 
120 
10 
Illowsky – Chapter 9 (65,71,77)
Background for problems 65 and 71: Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.
65. The null and alternative hypotheses are:
a. Ho: x ¯ = 4.5, Ha : x ¯ > 4.5
b. Ho: μ ≥ 4.5, Ha: μ < 4.5
c. Ho: μ = 4.75, Ha: μ > 4.75
d. Ho: μ = 4.5, Ha: μ > 4.5
71. The Type1error is:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher
77. An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Solve using the following steps, similar to AppendixE (Hypothesios Testing with One Sample Mean):
a. State the Null Hypothesis (H_{o}) and Alternate Hypothesis (H_{a})
b. Find the random variable X
c. State the distribution you will use and why ?
d. What is the test statistic (tvalue) ?
e. What is the Pvalue (probability) ?
f. Will you reject or not reject the Null Hypothesis and why ?
Illowsky – Chapter 10 (79,91,120)
79. A student at a fouryear college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the 35 two–year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 fouryear colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Test the hypothesis, assuming a 5% significance level. Solve using the following steps, similar to AppendixE (Hypothesios Testing with Two Sample Means):
a. State the Null Hypothesis (H_{o}) and Alternate Hypothesis (H_{a})
b. Find the random variable X (remember that X is the difference between the two sample means)
c. State the distribution you will use and why ?
d. What is the test statistic (tvalue) ?
e. What is the Pvalue (probability) ?
f. Will you reject or not reject the Null Hypothesis and why ?
91. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds. Test the hypothesis, assuming a 5% significance level. Solve using the following steps, similar to AppendixE (Hypothesios Testing with Two Sample Means):
a. State the Null Hypothesis (H_{o}) and Alternate Hypothesis (H_{a})
b. Find the random variable X (remember that X is the difference between the two sample means)
c. State the distribution you will use and why ?
d. What is the test statistic (tvalue) ?
e. What is the Pvalue (probability) ? HINT: Since the size of each sample set is different, the formula for the “degrees of freedom” is far more complex. See the formula on Page554.
f. Will you reject or not reject the Null Hypothesis and why ?
120. A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four new students. She records their 18hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as follows. Is the correct decision to Reject the Null Hypothesis or Not Reject the Null Hypothesis? Test the hypothesis, assuming a 5% significance level. Solve using the following steps:
a. State the Null Hypothesis (H_{o}) and Alternate Hypothesis (H_{a})
b. Find the random variable X. Consider we are testing “paired samples”.
c. State the distribution you will use and why ?
d. What is the test statistic (tvalue) ? Assume, the population mean of the differences = 0.
e. What is the Pvalue (probability) ?
f. Will you reject or not reject the Null Hypothesis and why ?

Player 1 
Player 2 
Player 3 
Player 4 
Mean score before class 
83 
78 
93 
87 
Mean score after class 
80 
80 
86 
86 
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