Question

Round all intermediate calculations to at least 4 decimal places) Based on the are predictions of 47 members of the National Association of Business Economists INABE the US gross domestic product (GDP) will expand by 32% in 2011 The Wall Street Journal May 21.2010) Suppose the sample standard deviation of their predictions was 1% Al a 5% significance level test if the mean forecast GDP of all NABE members is greater than 3% a. Select the null and the alternative hypotheses Ho = 3 HA #3 Hos 3 HAN 3 Ho #23HAN3 b. Calculate the value of test statistic (Round your answer to 2 decimal places.) Test statistic c. Approximate the p-value p-value < 0.01 0 01 s p-value < 0 025 0 025 s p value < 0 05 0.05 s p-value < 0 10 p-value 2 0 10 d. At the 5% significance level, can we conclude that the mean forecast GDP of all NABE members is greater than 3%? Yes, since we reject Ho Yes, since we do not reject Ho No, since we reject Ho No, since we do not reject Ho Type here to search

Answer 1

a.

The appropriate hypotheses is,

H0: $\mu$ $\le$ 3 , Ha: $\mu$ > 3

b.

Standard error of mean = S / $\sqrt{n}$ = 1 / $\sqrt{47}$ = 0.145865

Test statistic, t = (Observed mean - Hypothesized mean) / Std error

= (3.2 - 3) / 0.145865

= 1.37

c.

Degree of freedom = n-1 = 47 - 1 = 46

P-value = P(t > 1.37, df = 46) = 0.0887

0.05 $\le$ p-value < 0.10

d.

Since, p-value is greater than 0.05 significance level, we fail to reject H0 and do not conclude that $\mu$ > 3

No, since we do not reject H0