It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false, meaning it is different than advertised. She randomly test drives 36 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 20 feet. Use 5% significance.
Part 1
State the null hypothesis and the alternative hypothesis for testing that the average breaking distance is equal to 120 feet.
Part 2
State the critical value(s) for testing this hypothesis.
Part 3
Calculate the test statistic Z for testing this hypothesis
Part 4
State and support your conclusions
(A) We want to test whether the given statement that the mean equals 120 is false or not. So, it is a two tailed hypothesis
(B) Alpha level is 0.05 and using z distribution table, we get z critical values = -1.96 and 1.96 for two tailed hypothesis
(C) Given that mu = 120, xbar = 111, sigma = 20 and n = 36
test statistic z =
(D) It is clear that the z statistic is outside the range of z critical values, which means we can reject the null hypothesis as the z statistic is falling in the rejection region of Ho
We can conclude that the given statement is false at 0.05 significance level
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