Question

Research examining the effects of sun exposure has found that 15 min. of direct sun exposure often leads to greater feelings of energy compared to less than 15 min. of direct sun exposure. In a typical study into this phenomenon, a researcher obtains a sample of adults who spent at least 15 min. outside on a full sun day (no clouds) in the direct sunlight. The group is given a standardized energy test for which the general population of adults is 35.25 (higher scores indicate greater energy). The scores for the sample are as follows:

38,36,36,34,37,40,33,36,37,38.
Is this group of adults feeling more energy because of their sun exposure? Test at α=.05.
a. Use PSPP to test your hypothesis (include homogeneity of variance if appropriate). Test at a =.05. PDF print the output and submit the output to the dropbox (document name must be Sun.Output).
b. Is a test for homogeneity of variance needed? If so, use the PSPP output to evaluate. Explain the results of homogeneity of variance using a p value as support. If not needed answer NA.
c. State the test statistic results (including IV/DV descriptors) indicating significance and using the appropriate p value from the output to support your conclusion.
d. Calculate percentage of variance accounted for and describe the result in terms of the specific IV and DV.

Answer 1

The study is using statistical analysis to test if sun exposure increases energy levels, where a hypothesis test compares the sample mean to the general population mean energy score at a significance level of 0.05. Homogeneity of variance may not be needed for a single sample compared to a population mean, and the percentage of variance accounted for would show the effect of sun exposure on energy levels.

Step-by-step explanation:

The question relates to using the given data to conduct a hypothesis test concerning the effects of sun exposure on energy levels. The research hypothesis implies that more than 15 minutes of direct sun exposure increases energy levels compared to the general population mean energy score of 35.25. Positive effects of sunlight on energy levels can be attributed to factors like vitamin D synthesis and circadian rhythm regulation.

When conducting such a study, statistical tests such as t-tests are used to compare the sample mean to the population mean, and determine the statistical significance. The level of significance (α) is set at 0.05, meaning there is a 5% risk of concluding that an effect exists when it does not (Type I error). To perform this test, software like PSPP or SPSS is often used.

Homogeneity of variance is considered when comparing two or more groups to ensure that variances are similar across the groups. If the sample size is equal across groups, the violation of this assumption is less critical, but if the sample sizes are unequal, it becomes crucial to test for this. In this study, homogeneity of variance might not be relevant as there is only one group being compared to a known population mean.

Although not provided, the percentage of variance accounted for—a measure of effect size—would indicate the proportion of the variance in the dependent variable (energy levels) that is predictable from the independent variable (sun exposure).