Section 8.2, Exercise #20, p. 458 - (a) identify the claim and state H 0 and H a

Question

Section 8.2, Exercise #20, p. 458 -

(a) identify the claim and state H0 and Ha,

(b) find the critical value(s) and identify the rejection region(s),

(c) find the standardized test statistic z,

(d) decide whether to reject or fail the null hypothesis, and

(e) interprets the decision in the context of the original claim. If convenient, use technology to solve the problem. In each exercise, assume the populations have approximately normal distributions.

20. Annual Wages A random sample of 17 residents of Escambia County in Florida has a mean annual income of $36,700 and a standard deviation of $7800. In Miami-Dade County in Florida, a random sample of 18 residents has a mean annual income of $34,700 and a standard deviation of $7375. Test the claim = 0.01 that the mean annual incomes in Escambia and Miami-Dade counties are not the same. Assume the population variances are normal.

Explanation / Answer

a) H0: mu1=mu2 (mean annual income in Escambia nd Miami-Dade counties are same)

H1: mu1 not equal to mu2 (mean annual income in Escambia nd Miami-Dade counties are not the same).

b) DF=n1+n2-2=17+18-2=33, alpha=0.05, t critical is 2.0345. [t test is suitable, as sample size is less than 30 in each case]

Reject null hypothesis, if H0>2.0345.

c) The technology calculated t test statisc value is 0.78.

The test statistic do not fall in critical region. Fail to reject null hypothesis. There is not sufficient sample evidence to conclude that mean annual incomes inEscambia and Miami-Dade counties are not the same.

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