Question

In: Operations Management

Suppose we have two sets of prediction for the inflation rate for next year: one from...

Suppose we have two sets of prediction for the inflation rate for next year: one from a random sample of Fortune 500 firms and another from a random sample of university economists. At 0.05 level can it be claimed that on the average university educators are predicting a higher inflation rate for next year than the major private businesses?

Fortune 500 Firms	4.3%	3.8%	6.0%	4.4%	5.1%	5.6%	4.2%	6.1%	4.5%	4.0%
University Economists	4.4%	5.9%	7.0%	5.1%	5.9%	7.2%	6.3%

Formulate the hypothesis (H₀ and H_a) and describe each in nontechnical language and in mathematical form. (5 pts)

Show the mean, rejection region, and the critical value(s) on the following graph. (6 pts)

Show the equation for computing the standard error.

What is your decision and why? (4 pts.)

Provide a conclusion in non-technical language (5 pts)

Expert Solution

(a)

H0: μ1 = μ2
Ha: μ1 > μ2

Where 'μ' is the population parameter for the average inflation rate and 1 and 2 are the suffixes for university experts and Fortune 500 firms (i.e. private businesses) respectively.

The null hypothesis means that there is a status quo that both the population parameters are equal. The alternative hypothesis is the claim that the population average inflation for 1 is more than that of 2 and this we will test using the hypothesis.

(b)

The difference in sample means (center of the graph) = x̄1 - x̄2 = 0.0597 - 0.0480 = 0.0117

The variances are close enough to assume equal variances. The standard error will be written as:

where:

So,

Sp = (((7-1)*0.0099^2 + (10-1)*0.0084^2) / (7+10-2))^0.5 = 0.0090

Standard error (Se) = 0.0090 * (1/7 + 1/10)^0.5 = 0.0045

Alpha = 0.05

The corresponding critical value, t_crit= T.INV(0.95, 7+10-2) = 1.75

The test statistic, t_test = (x̄1 - x̄2) / Se = 0.0117 / 0.0045 = 2.60

(c)

Since t_test > t_crit, it falls in the rejection region. So, the null hypothesis is rejected and it is affirmed by the test that μ1 > μ2 at a 5% significance level.

(d)

In plain language, the two samples show that the population average inflation for the university experts' reported inflation value is significantly more than that reported by the industry professional.

keosha answered 21 hours ago

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