In: Statistics and Probability
In #29-32, use the following information. Use a 0.025 level of significance to test the claim that vehicle speeds at a certain location have a mean above 55 km/h . A random sample of 50 vehicles produces a mean of 61 3. km/h and standard deviation of 3 3. km/h .
29. Give the null hypothesis in symbolic form. (a) H0 :µ > 55 (b) H0 :µ ≥ 55 (c) H0 :µ ≤ 55 (d) H0 :µ < 55 (e) H0 :µ = 55
30. Determine the appropriate test statistic. (a) z = 12.1 (b) z = 13.5 (c) p = 10.2 (d) p = 4.28 (e) z = 8.31
31. Find the appropriate critical value(s). (a) z = −1.96 (b) z = 1.96 (c) z = −1.96, z = 1.96 (d) z = −2.24, z = 2.24 (e) t = −1.96
32. Make the appropriate decision. (a) Reject H0 (b) Fail to reject H
Solution :
29) This will be a right tailed test because the alternative hypothesis is showing a specific direction
This is the right tailed test,
The null and alternative hypothesis is ,
H0 : = 55
Ha : > 55
= 61.3
= 3.3
n = 50
30) Test statistic = z =
= ( - ) / / n
= (61.3 - 55) / 3.3 / 50
Test statistic = z = 13.5
31) = 0.025
This is the right tailed test,
P(z > z ) = 0.025
= 1 - p( z < z ) = 0.025
= p( z < z ) = 1 - 0.025
= p( z < z ) = 0.975
= p( z < 1.96 ) = 0.975
z* critical value = 1.96
32) (a) Reject H0 , because test statistic > critical value