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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.

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9 votes

Answer:

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

User Galen
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