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Based on the average predictions of 50 economists, the U.S. gross domestic product (GDP) will expand by 2.5% 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%.
a. Select the null and the alternative hypotheses.

multiple choice 1
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.)



c. Find the p-value.

multiple choice 2
p-value 0.10
p-value < 0.01
0.01 p-value < 0.025
0.025 p-value < 0.05
0.05 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%?

multiple choice 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.

rev: 10_13_2020_QC_CS-234700, 11_27_2020_Q

Respuesta :

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The null and hypothesis test; test statistic and the conclusion of the hypothesis are :

  • [tex] H_{0} : \mu\geq 3 ; H_{1} : \mu < 3[/tex]

  • Test statistic = -1.7678

  • Pvalue < 0.05

  • Yes, since we reject H0

The hypothesis :

  • [tex] H_{0} : \mu \geq 3 [/tex]

  • [tex] H_{1} : \mu < 3 [/tex]

The test statistic :

[tex]\frac{\bar{x} - \mu}{\frac{σ}{\sqrt{n}}}[/tex]

Substituting the values into the equation :

[tex]\frac{2.5 - 3.0}{\frac{2}{\sqrt{50}}} = -1.7678[/tex]

The Pvalue, using a Pvalue calculator ; 1 - tailed ; 10% level of significance (0.10) = 0.038

Hence, Pvalue < 0.05

3.) At 10% level of significance ;

We compare the Pvalue and the α

α = 10% = 0.10

Since, Pvalue < α (0.038 < 0.10) ; then the result is significant.

Therefore, the result is significant at α = 0.10

Learn more : https://brainly.com/question/25279120

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