Homeowners claim that the mean speed of automobiles traveling on their street is greater than the speed limit of 35 miles per hour. A random sample of 120 automobiles has a mean speed of 37 miles per hour and a standard deviation of 4 miles per hour. Using a significance level of 0.05, what is the test statistic for this hypothesis test?
To determine the test statistic for this hypothesis test, you need to perform a one-sample t-test.
The null hypothesis, denoted as H0, states that the mean speed of automobiles on the street is equal to or less than the speed limit of 35 miles per hour.
The alternative hypothesis, denoted as Ha (or sometimes H1), states that the mean speed of automobiles on the street is greater than 35 miles per hour.
Since you have the sample mean (37 miles per hour), sample standard deviation (4 miles per hour), and sample size (120), you can calculate the test statistic using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values:
t = (37 - 35) / (4 / sqrt(120))
Calculating the value inside the square root first:
sqrt(120) ≈ 10.954
Now back to the formula:
t = (37 - 35) / (4 / 10.954)
t = 2 / (4 / 10.954)
t = 2 / 0.911
t ≈ 2.19
Therefore, the test statistic for this hypothesis test is approximately 2.19.