In: Statistics and Probability
Hypothesis Tests with Z-statistics
Disregarding the posted speed limit, drivers in a residential area would drive at an average of 35 MPH with a standard deviation of 7 MPH. In an effort to reduce the speeds driven, the city installed speed bumps. After gathering data from 42 drivers, it was found that they drove at an average speed of 30 MPH.
a. Who are the groups being compared/tested?
b. What are the null and research hypotheses?
c. what are the numbers needed for the z statistic?
d. What is the z statistic?
e. For a two tailed test at .05 significance, the critical area is
+/- 1.96. What decision do we make?
a. Who are the groups being compared/tested?
Answer: A group of 42 drivers is being compared for the population of drivers for their average speed.
b. What are the null and research hypotheses?
Null hypothesis: H0: The drivers in a residential area would drive at an average of 35 MPH.
Alternative hypothesis: Ha: The drivers in a residential area would drive at an average less than 35 MPH.
c. what are the numbers needed for the z statistic?
From given data, we have
µ = 35
Xbar = 30
σ = 7
n = 42
d. What is the z statistic?
The test statistic formula is given as below:
Z = (Xbar - µ)/[σ/sqrt(n)]
Z = (30 - 35)/[7/sqrt(42)]
Z = -4.6291
e. For a two tailed test at .05 significance, the critical area is +/- 1.96. What decision do we make?
From above part, we have Z < -1.96, so we reject the null hypothesis.
There is sufficient evidence to conclude that the drivers in a residential area would drive at an average less than 35 MPH.