(a) Write the claim mathematically and identify Upper H 0H0 and Upper H Subscrip
ID: 3134786 • Letter: #
Question
(a) Write the claim mathematically and identify Upper H 0H0 and Upper H Subscript aHa. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis. In a sample of 10001000 home buyers, you find that 453453 home buyers found their real estate agent through a friend. At alphaequals=0.060.06, can you reject the claim that 4545% of home buyers find their real estate agent through a friend? (a) Which of the following correctly states Upper H 0H0 and Upper H Subscript aHa?
Explanation / Answer
a)
Formulating the null and alternatuve hypotheses,
Ho: p = 0.45
Ha: p =/= 0.45 [ANSWER]
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b)
As alpha = 0.06, two tailed,
zcrit = -1.88, 1.88
Hence, reject Ho when |z| > 1.88. [ANSWER]
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c)
As we see, the hypothesized po = 0.45
Getting the point estimate of p, p^,
p^ = x / n = 0.453
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.015732133
Getting the z statistic,
z = (p^ - po)/sp = 0.190692518 [ANSWER]
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d)
As |z| < 1.88, we FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER]
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There is no significant evidence that not 45% of home buyers find their real estate agent through a friend at 0.06 level.
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