Question

-6 points You may need to use the appropriate appendix table or technology to answer this question. Consider the following hypothesis test. ASWSBE 139E.011. 3. + Ho' μ-15 Ha: μ * 15 A sample of 50 provided a sample mean of 14.09. The population standard deviation is 3 (a) Find the value of the test statistic. (Round your answer to two decimal places.) (b) Find the p-value. (Round your answer to four decimal places.) p-value (c) At α-0.05, state your conclusion. 0 Reject Ho. There is sufficient evidence to conclude that,# 15. 0 Reject H0. There is insufficient evidence to conclude that μ * 15. O Do not reject Ho. There is sufficient evidence to conclude that μ # 15. O Do not reject Ho. There is insufficient evidence to conclude that μ * 15. (d) State the critical values for the rejection rule. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic s test statistic 2 State your conclusion. 0 Reject H0. There is sufficient evidence to conclude that μ * 15. 0 . Reject H0. There is insufficient evidence to conclude that μ # 15 Do not reject Ho. There is sufficient evidence to conclude that μ # 15. Do not reject H0. There is insufficient evidence to conclude that μ # 15.

Answer 1

Given that, sample size ( n ) = 50

sample mean = 14.09

population standard deviation = 3

The null and alternative hypotheses are,

Ho : μ = 15

$H_a: \mu \neq 15$

a) Test statistic is,

14.09 15 =-2.14

b) p-value = 2 * P(Z < -2.14) = 2 * 0.0162 = 0.0324

=> p-value = 0.0324

c) Since, p-value = 0.0324 <

a-0.05

=> Reject H₀. There is sufficient evidence to conclude that

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d) critical values at are, z^* = ± 1.96

a-0.05

Rejection rule is,

test statistic $\leq$ -1.96

test statistic $\geq$ 1.96

Since, test statistic = -2.14 < -1.96

=> Reject H₀. There is sufficient evidence to conclude that

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