Find the t-values that form the boundaries of the critical regions for a two-tai
ID: 3219193 • Letter: F
Question
Find the t-values that form the boundaries of the critical regions for a two-tailed test with a=.05 for each of the following sample size (N) values.
(Hint: For a two-tailed test, we need two critical values for the significance areas in the two tails. Note that you will need to figure out df for the t table.)
N = 10 (1 point)
N = 20 (1 point)
N = 30 (1 point)
Based on the answers for (a) to (c) above, what can you glean about the relationship between sample size and critical value? (1 point)
Q2) One-Sample t-Test (Total 19 points)
According to the statistics from 2009, the broadcast networks in American averaged ( ) 13.50 minutes of commercials during a one-hour program. I was curious whether the commercial time is significantly different now compared to 2009. So I measured the commercial time during a one-hour period during primetime on 9 different networks and recorded the number of minutes in the table below. I will assume that the commercial time across all the broadcast networks in America is normally distributed and I will perform a two-tailed hypothesis test with = .05.
TV Network
Number of minutes of commercials in a one-hour program
1
13
2
13.5
3
15
4
14.25
5
14.5
6
14.25
7
13.25
8
16
9
16.75
Identify the outcome (dependent) variable and the independent variable (that differentiate the two populations being compared). (1 pt for DV, 1 pt for IV)
What would be the null and alternative hypotheses in both words and symbol notations (1 for each hypothesis in words, 1 for each hypothesis in notation, total 4 points)
Calculate the mean number of minutes of commercial from the sample (.5 for formula/work, .5 for answer)
Estimated the standard deviation of the comparison population (1 for formula/work, 1 for answer)
Calculate the standard error (standard deviation of the sampling distribution) (1 for formula/work, 1 for answer)
Calculate the t statistic for the sample (1 for formula/work, 1 for answer)
Determine the critical t value(s) (1 point)
Compare the t statistic with the critical value (1 point)
Make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” (1 point)
Interpret the result in 1-2 sentences (you may restate the hypothesis accepted or explain it in your own words) (1 point)
Calculate the standardized effect size of this hypothesis test (1 point for formula/work; 1 point for result)
Q3) Paired-Samples t Test
A physician at the veterans’ hospital has been prescribing an MAOI (monoamine-oxidase inhibitor) drug for his veteran patients diagnosed with PTSD. He wondered if MAOI would affect the frequency of nightmares for this patient population. He first asked 10 of his patients with PTSD to record each incident of a nightmare for 1 month before treatment. Participants were then given the MAOI medication for 6 weeks, and then they were again asked to record each occurrence of a nightmare for a month.
Part I. (20 points total)
The physician would like to conduct a two-tailed hypothesis test with = .10 to see if MAOI made a significant difference in the number of nightmares. Below are the patients’ data from before and after treatment:
Number of Nightmares within a Month
Subject
Before MAOI treatment
After MAOI treatment
1
6
3
2
1
0
3
3
4
4
5
5
5
7
2
6
4
4
7
2
3
8
4
3
9
2
2
10
8
6
Calculate the difference score by subtracting the “before” score from the “after” score. Fill in the column in the table below for “difference score.” (1 point, deduct .5 for each error up to 1 points)
Subject
Difference score (after – before)
1
2
3
4
5
6
7
8
9
10
Identify the outcome (dependent) variable and the independent variable (that differentiate the two populations being compared). (1 pt for DV, 1 pt for IV)
What would be the null and alternative hypotheses in both words and symbol notations (1 for each hypothesis in words, 1 for each hypothesis in notation, 4 points total)
Calculate the mean from the sample of the difference scores (.5 for formula/work, .5 for answer)
Estimated the standard deviation of the comparison population (that represents the null hypothesis) (1 for formula/work, 1 for answer)
Calculate the standard error (standard deviation of the sampling distribution) (1 for formula/work, 1 for answer)
Calculate the t statistic for the sample (1 for formula/work, 1 for answer)
Determine the critical value(s) (1 point)
Compare the t statistic with the critical value (1 point)
Make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” (1 point)
Interpret the result in 1-2 sentences (you may restate the hypothesis accepted or explain it in your own words) (1 point)
Calculate the standardized effect size of this hypothesis test (1 point for formula/work; 1 point for result)
Part II. (7 points + extra credit 3 points)
The physician actually has a good reason to hypothesize the direction of the potential drug effect because the drug has been developed specifically to reduce PTSD symptoms. So he decided to run another hypothesis on the same data, but using a one-tailed test with the same = .10 to see if the patients have significantly lower frequency of nightmares after the treatment.
What would be the null and alternative hypotheses in both words and symbol notations (1 for each hypothesis in words, 1 for each hypothesis in notation, 4 points total)
The calculated t statistic remains the same as in Part I, but we need to find the critical t value based on the new test. (1 point)
Compare the t statistic with the critical value (.5 point)
Make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” (.5 point)
Interpret the result in 1-2 sentences (you may restate the hypothesis accepted or explain it in your own words) (1 point)
TV Network
Number of minutes of commercials in a one-hour program
1
13
2
13.5
3
15
4
14.25
5
14.5
6
14.25
7
13.25
8
16
9
16.75
Explanation / Answer
1) a) T critical value 2.262 and 2.262 on 9 degrees of freedom at 5% rejection level
b) T critical value -2.093 and 2.093 on 19 degrees of freedom at 5% rejection level
c) T critical value -2.045 and 2.045 on 29 degrees of freedom at 5% rejection level
2)
a) H0: µ = 13.5
H1: µ 13.5
b) Mean = x / n = 14.5
Standard deviation 's' = x2/n - Mean2 = 1.25
Standard error = s/n = 1.25 / 3 = 0.4167
c)
T test statistic = xbar - µ / [ s/n]
= 14.5 - 13.5 / [1.25/9]
= 2.4
d) T critical value -2.306 and 2.306 on 8 degrees of freedom at 5% rejection level
e) Now T test statistic > 2.306
f) Decision : Reject H0
g)
We conclude that there is suffiecient evidence the broadcast networks in American averaged ( µ) 13.50 minutes of commercials during a one-hour program
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