Answer: t=5.59
Step-by-step explanation:
We assume that the money in wallets of women and men are normally distributed.
Given : Sample size of females : [tex]n_x=16[/tex]
Sample mean : [tex]\overline{X}=22.30[/tex]
Standard deviation : [tex]\sigma_x=3.20[/tex]
Sample size of males : [tex]n_y=16[/tex]
Sample mean : [tex]\overline{Y}=22.30[/tex]
Standard deviation : [tex]\sigma_y=9.60[/tex]
Since sample size is small (<30), so we use t-test.
The test static for difference of two population mean is given by :-
[tex]t=\dfrac{\overline{X}-\overline{Y}}{\sqrt{\dfrac{\sigma_x}{n_x}+\dfrac{\sigma_y}{x_y}}}[/tex]
[tex]=\dfrac{22.30-17.30}{\sqrt{\dfrac{3.20}{16}+\dfrac{9.60}{16}}}\\\\=5.59016994375\approx5.59[/tex]
Hence, the test statistic for the researcher’s hypothesis is : t=5.59
