A psychology researcher has a theory that predicts women will tend to carry more cash than men. A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20, while 16 males had a mean of $17.30 with a standard deviation of $9.60. The test statistic for the researcher's hypothesis is:

Question

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To test the hypothesis, we can use a two-sample t-test with unequal variances. The test statistic is calculated as:

t = (mean_female - mean_male) / sqrt[(s_female^2/n_female) + (s_male^2/n_male)]

Plugging in the numbers, we get:

t = (22.30 - 17.30) / sqrt[(3.20^2/16) + (9.60^2/16)]

t = 5 / 3.772

t = 1.326

This value is greater than the critical t-value with 28 degrees of freedom at the 0.05 level (t = 2.048). Therefore, we can reject the null hypothesis and conclude that there is evidence to support the idea that women tend to carry more cash than men.

The closest answer choice is D, which is the t-value rounded to three decimal places.

A Psychology Researcher Has a Theory That Predicts Women Will