Based on the average predictions of 55 economists, the U.S. gross domestic product (GDP) will expand by 2.6% this year. Suppose the sample standard deviation of their predictions was 2%. At the 10% significance level, test if the mean forecast GDP of all economists is less than 3%. (You may find it useful to reference the t table.)
a. Select the null and the alternative hypotheses.
H0: μ = 3; HA: μ ≠ 3
H0: μ ≤ 3; HA: μ > 3
H0: μ ≥ 3; HA: μ < 3
b. Calculate the value of test statistic. (Round final answer to 4 decimal places.)
Test statistic: -0.9888
c. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
d. At the 10% significance level, can we conclude that the mean forecast GDP of all economists is less than 3%?
No, since we do not reject H0.
No, since we reject H0.
Yes, since we do not reject H0.
Yes, since we reject H0.