Question

6. (1) t, z, (2) equal to less than not contained within greater than (3) z t (4) Reject Do not reject (5) is is not (6) is greater than does not equal is less than is equal to Consider the following hypothesis test. Given that n = 84, σ = 8, x = 49.9, and α = 0.01, complete parts a through d below. H : 0 μ ≤ 47 H : A μ > 47 a. State the decision rule in terms of the critical value(s) of the test statistic. Reject the null hypothesis if the calculated value of the test statistic, (1) is (2) the critical value(s), . Otherwise, do not reject the null hypothesis. (Round to two decimal places as needed. Use a comma to separate answers as needed.) b. State the calculated value of the test statistic. (3) = (Round to two decimal places as needed.) c. State the appropriate p-value. p-value = (Round to three decimal places as needed.) d. State the conclusion. (4) the null hypothesis. There (5) sufficient evidence at to conclude the population mean (6) . α = 0.0

Answer 1

for 0.01 level with right tail test , critical z=			2.33	(from excel:normsinv(0.01)
Decision rule:reject Ho if test statistic z>2.326

Otherwise, do not reject the null hypothesis.
b)

population mean μ=		47
sample mean 'x̄=		49.900
sample size    n=		84
std deviation σ=		8.000
std error ='σx=σ/√n=8/√84=		0.8729
z statistic= ='(x̄-μ)/σx=(49.9-47)/0.873=		3.32

c)

p value        =

0.000

(from excel:1*normsdist(-3.32)

d)

reject the null hypothesis

There is sufficient evidence at to conclude the population mean is greater than 47 at α =0.01