Question

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:

Answer 1

Answer: t=5.59

Explanation:

We assume that the money in wallets of women and men are normally distributed.

Given : Sample size of females :
`n_x=16`

Sample mean :
`\overline{X}=22.30`

Standard deviation :
`\sigma_x=3.20`

Sample size of males :
`n_y=16`

Sample mean :
`\overline{Y}=22.30`

Standard deviation :
`\sigma_y=9.60`

Since sample size is small (<30), so we use t-test.

The test static for difference of two population mean is given by :-

`t=\frac{\overline{X}-\overline{Y}}{\sqrt{(\sigma_x)/(n_x)+(\sigma_y)/(x_y)}}`

`=\frac{22.30-17.30}{\sqrt{(3.20)/(16)+(9.60)/(16)}}\\\\=5.59016994375\approx5.59`

Hence, the test statistic for the researcher’s hypothesis is : t=5.59