Question

Brooke is moving out of her parents’ house into her first apartment. While packing she realizes she has a lot of shoes – 42 pair, in fact. She wonders if most women have as many shoes as she does, so for her experimental psychology project she sends surveys to120 women from her college and asks how many pairs of shoes they have. She finds that, on average, the women have15 pair of shoes (sd =2.50). Given this information, does Brooke have statistically more shoes than women in general? Complete the six steps of hypothesis testing by hand and perform the appropriate statisticaltest using SPSS. Then, writean APA formatted 4-part results section.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 15
Alternative hypothesis: u > 15

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.2282
DF = n - 1

D.F = 119
t = (x - u) / SE

t = 118.31

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 118.31

Thus the P-value in this analysis is less than 0.001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that Brooke have statistically more shoes than women in general.