It is reported that 20% of a certain type of holiday light set will fail if the

Question

It is reported that 20% of a certain type of holiday light set will fail if the temperature dips to 0 degree F. In a test, each of a random sample of 100 such light sets was subjected to a temperature of 0 degree F. Let X be the count of the tested lights sets that fail. Let p be the actual proportion of holiday lights sets that will fail when subjected to a temperature of 0 degree F. We believe that that actual proportion of those light sets that will fail when subjected to a temperature of 0 degree F is greater than 20%, so we will make this our test (alternative) hypothesis. Upon performing the temperature test on 100 holiday lights sets we discover that 27 of them fail. (a) State the specific hypotheses that will be tested. (b) What is the point estimate for p? (c) What is the test statistic for this hypothesis test? (type and value) (d) What is the p-value for this hypothesis test?

Explanation / Answer

a)
Null hypothesis: P = 0.20
Alternative hypothesis: P > 0.20

b) Point estimate for P is 0.20

c)

p = 27 / 100 = 0.27 , n =100

= sqrt[ P * ( 1 - P ) / n ]
= sqrt [(0.2 * 0.8) / 100]
= sqrt(0.0016) = 0.04
z = (p - P) /
= (.27 - .20)/0.04
= 1.75

d) p value is calculated using z = 1.75 at 0.05 significance level.
p value = 0.04005

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