A researcher uses a matched- subjects design to investigate whether single people who own pets are generally happier than single people without pets. A mood inventory questionnaire is administered to a group of 20 to 29 year old non pet owners and a similar age of pet owners. The pet owners are matched one to one with the non- pet owners doe income, number of close friendships, and general health.
a. Is there a significant difference in the mood scores for non-pet owners versus pet owners? Test with a=.05 for two tails
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To determine if there is a significant difference in the mood scores between non-pet owners and pet owners, you can use a matched-subjects design and perform a paired samples t-test. This test allows us to compare the means of two dependent groups.
Here's how you can conduct the analysis to find the answer to your question:
1. Set up your null and alternative hypotheses:
- Null hypothesis (H0): There is no significant difference in the mood scores between non-pet owners and pet owners.
- Alternative hypothesis (Ha): There is a significant difference in the mood scores between non-pet owners and pet owners.
2. Calculate the difference in mood scores for each matched pair by subtracting the mood score of the non-pet owner from the corresponding pet owner. This will give you a set of difference scores.
3. Compute the mean and standard deviation of the difference scores.
4. Use a t-test to determine if the mean difference in mood scores is statistically significant. Given that you have a small sample size and don't assume the population follows a normal distribution, you should use a paired samples t-test.
5. Set your significance level (α) to 0.05 for a two-tailed test. This means you're looking for evidence against the null hypothesis in both directions.
6. Perform the t-test using software like Excel, SPSS, or an online statistical tool. Input the difference scores and perform the t-test. The output will provide the t-value, degrees of freedom, and the p-value associated with the test.
7. Compare the p-value to the significance level (α). If the p-value is less than α (p < 0.05), you can reject the null hypothesis. This means there is a statistically significant difference in mood scores between non-pet owners and pet owners. If the p-value is greater than α (p > 0.05), you fail to reject the null hypothesis, indicating that there is no significant difference in mood scores between the two groups.
Remember, statistical significance does not necessarily imply practical significance. You should also consider the effect size, confidence intervals, and the context of your research when interpreting the results.