Question

For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51 nonvegetarian students and a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students. When we use software to compare the means with a significance test, we obtain the following printout.Variances T DF Prob>|T|Unequal 2.9146 41.9 0.006Interpret the P-value, in context, based on its definition.

Answer 1

From the test give in the question it is obvious that there is enough evidence to show that population mean varies for vegetarian and non-vegetarian

The P-value helps affirm the null hypothesis claims,The P-value attains values relatively as large as that which exists in the sample given,if the null hypothesis is right

Explanation:

From the question we are told that

Sample mean
`\=x_1=3.18`

Standard deviation
`\delta_! =1.72`

Sample size
`n_1 =51`

Sample mean
`\=x_2=2.22`

Standard deviation
`\delta_2 =0.67`

Sample size
`n_2=20`

Generally this is a two tailed test

therefore

Null hypothesis =
`h_0 :P_v_e_g= P_n_o_n_v_e_g`

Alternative hypothesis
`H_a : P_v_e_g \\eq P_n_o_n_v_e_g`

From the test give in the question it is obvious that there is enough evidence to show that population mean varies for vegetarian and non-vegetarian

The P-value helps affirm the null hypothesis claims,The P-value attains values relatively as large as that which exists in the sample given,if the null hypothesis is right