Question

Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the mathematical symbols. A psychologist is interested in exploring whether or not male and female college students have different driving behaviors. She opted to focus on the fastest speed ever driven by an individual. Therefore, the particular statistical question she framed was as follows: Is the mean fastest speed driven by male college students different than the mean fastest speed driven by female college students? A sample of 34 men had a mean speed of 105.5 mph with a standard deviation of 20.1 mph, while a sample of 29 women had a mean speed of 90.9 mph with a standard deviation of 12.2 mph. Use α = .05 and assume that population variances are equal.

Answer 1

H₀:

H₁:

The pooled variance(s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

                                  = (33 * (20.1)^2 + 28 * (12.2)^2)/(34 + 29- 2)

                                  = 286.883

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

                            = (105.5 - 90.9)/sqrt(286.883/34 + 286.883/29)

                            = 3.41

DF = 34 + 29 - 2 = 61

At = 0.05, the critical values are t^* = +/- 2

Since the test statistic value is greater than the upper critical value (3.41 > 2), so we should reject the null hypothesis.

So ata alpha = 0.05, there is sufficient evidence to conclude that the mean fastest speed driven by male college students different than the mean fastest speed driven by female college students.