Normal Distribution Hypothesis Test Answer Check

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#1
The ability to withstand pain is known to vary from individual to individual.

In a standard test, a tiny electric shock is applied to the finger until a tingling sensation is felt. When this test was applied to a random sample of 10 adults, the times recorded in seconds, before they experienced a tingling sensation were:

4.2, 4.5, 3.9, 4.4, 4.1, 4.5, 3.7, 4.8, 4.2, 4.2

Test, at the 5% level, the hypothesis that the mean time before an adult would experience a tingling sensation is 4 seconds. The times are known to be normally distributed with a standard deviation of 0.2 seconds.

Mean = 4
Standard deviation = 0.2
n = 10
mean of sample = 4.25

H0: Mean = 4
H1: Mean doesn't = 4
Significance level = 5%
critical values = +- 1.96
test statistic = (4.25-4)/((0.2)/(root 10))
= 1.25root 10 = 3.95

3.95 > 1.96

Reject H0, the test statistic lies in the critical region. There is sufficient evidence at 5% significance level to suggest that the mean time before an adult would experience a tingling sensation is greater than 4 seconds.

This is my answer, however, it says in the textbook:
"ts = 3.95 c.v. = +- 1.96
Conclusion: Mean time not (greater than) 4s"

But how is this the case? Am I wrong or is the textbook wrong?
0
1 year ago
#2
(Original post by TAEuler)
This is my answer, however, it says in the textbook:
"ts = 3.95 c.v. = +- 1.96
Conclusion: Mean time not (greater than) 4s"

But how is this the case? Am I wrong or is the textbook wrong?
Textbook's in error. ts is clearly in the critical region.
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