Hypothesis Testing (Coursework Sample)

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Professor’s Name
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CP. 7 ASSIGNMENT
In this assignment we test the claim in an article that young adults on average own three pairs of jeans. We want to test this against a counter claim that they actually own more than three pairs of jeans on average.
To accomplish this, we will use a sample of 25 responses from young adults between 18 years to 35 years who were asked how many pairs of jeans they own.
Sample Selection
We asked 25 randomly selected young adults a question to state how many pairs of jeans they owned. The responses from these randomly selected respondents were recorded as shown below:
Sample Data

2

3

3

5

1

6

4

1

7

3

7

3

2

4

7

2

4

1

4

6

2

7

5

7

5

The sample mean and standard deviations to the nearest pair of trousers areM=4.040 and SD=2.071, respectively.
A larger sample could have eliminated the possible selection biases that might have been encountered during the random selection of participants.
Hypothesis Testing
Conditions for Inference
We first start by checking that the conditions for inference are met for the sample that has been drawn. The following are the conditions for inference:
1 Independent Condition. The sample drawn is less than of 25 is less than 10% of the possible population size of all the young adults who could have been interviewed nand as such we can assume independence of the sample drawn.
2 Normality Condition. The population from which we draw our sample from is assumed to be normal hence the sample is equally assumed to be normal.
3 Random Condition. We have picked the young adults to be interviewed at randomly from the population hence the normally condition is met.
Conducting an Hypothesis Testing
We conduct a hypothesis of the claim that young adults on average own three pairs of jeans against an alternative that they own more than three pairs. The following are the steps for testing this hypothesis:
Step 1: State the Null and Alternative Hypotheses
μ= the mean number of pairs of jean trousers owned by young adults
α=0.05 is the significance level
Sample Size, n=25
Sample Mean, X=4.040
Sample Standard Deviation, SD=2.071
H0:μ=3, the mean pair of jeans owned by young adults is equal to 3
H1:μ>3, the mean pair of jeans owned by young adults is greater than 3
Step 2: Define the Test to be conducted
We will carry out the one-tailed one sample t-test. This is because we have a sample population which is less than 30 and we are given the sample standard deviation. The test will be a right tailed test since the alternative claim is that the mean number is greater than the hypothesized mean. Below is a figure showing the area of rejection on the standard normal curve at an alpha level of 0.05 (Confidence Level).
Step 3: Conduct the Test
We conduct a one sample t-test using the Statistical Software MiniTab Express with the above stated Null and Alternative Hypothesis. The following are the test results from MiniTab Express:
Descriptive Statistics

NMeanStDevSE Mean95% CI for μ254.04002.0