The time needed for college students to complete a certain paper and pencil maze follows a Normal distribution with a population mean of 80 seconds and a population standard deviation of 16 seconds. You wish to see if the mean time µ is changed by meditation, so you have a random sample of 12 college students meditate for 30 minutes and then complete the maze. It takes them an average of x = 73.3 seconds to complete the maze, with a standard deviation of 14.2 seconds. Use this information to test the hypotheses: H0: µ = 80, Ha: µ (does not =) 80 at the significance level α = 0.02.
a. Calculate the test statistic for this test.
b. Calculate the p-value for this test.
c. Is the null hypothesis rejected? Why or why not? Is this data statistically significant at the α = 0.02 level?
Part a)
To Test :-
H0 :- µ = 80
H1 :- µ ≠ 80
Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 73.3 - 80 ) / ( 16 / √( 12 ))
Z = -1.4506
Part b)
P value = 2 * P ( Z > 1.4506 ) = 2 * 1 - P ( Z < 1.4506 ) = 0.1469 ( From Z table )
Part c)
Reject null hypothesis if P value < α = 0.02 level of
significance
Since 0.1469 > 0.02, hence we reject null
hypothesis
Result :- We fail to reject null
hypothesis
The time needed for college students to complete a certain paper and pencil maze follows a...
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