Question

The mean time between failures for a type of radio used in light aircraft is 420 hours. Fifteen of this type of radio were modified to improve reliability, and test data showed a mean of 442.2 hours with a standard deviation of 44.0 hours.

a. Use a 5% level of significance to test the claim that the mean reliability has improved.

b. If you use a 1% level of significance, does this change your conclusion? Explain

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 420
Alternative Hypothesis, Ha: μ > 420

Rejection Region
This is right tailed test, for α = 0.05 and df = 14
Critical value of t is 1.76.
Hence reject H0 if t > 1.76

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (442.2 - 420)/(44/sqrt(15))
t = 1.954

P-value Approach
P-value = 0.0355
As P-value < 0.05, reject the null hypothesis.

b)

yes, conclusion will change

P-value Approach
P-value = 0.0355
As P-value > 0.01, fail to reject the null hypothesis.