Question

A psychological 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


1.976


1.250


1.504

Answer 1

Answer:

The test statistic for the researcher's hypothesis is 1.976

Step-by-step explanation:

The standard error (SE) is,

$SE=\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2} }$

Given that,

$\bar x = 22.30,S_1=3.20\\\\\bar x=17.30,S_2=9,60\\\\n_1=16,n_2=16$

$SE =\sqrt{\frac{(3.20)^2}{16} +\frac{(9.60)^2}{16} } \\\\=\sqrt{(0.64+5.76)} \\\\=2.53$

The test statistic is obtained below:

$t=\frac{( \bar x_1 - \bar x_2)}{\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } }$

$=\frac{(22.30-17.30)}{2.53} \\\\=\frac{5}{2.53} \\\\=1.976$

Therefore, the test statistic for the researcher's hypothesis is 1.976