Question

44.

You may need to use the appropriate technology to answer this question. Consider the follovring hypothesis test. A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.01. (a)x44 and s5.1 Find the value of the test statistic. (Round your ansvwer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion. O Do not reject Ho. There is sufficient evidence to conclude that μ 45. O Do not reject Ho. There is insufficient evidence to conclude that μ 45. O Reject Ho. There is sufficient evidence to conclude that μ 45. O Reject Ho. There is insufficient evidence to conclude that μ 45.

Answer 1

Solution :

$\mu$= 45

n = 36

a) $\bar x$ = 44

s = 5.1

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ ≥ 45

H_a : $\mu$ < 45

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (44-45) /5.1 / $\sqrt$ 36

= -1.176

P(z <-1.176 ) = 0.1237

P-value = 0.1237

$\alpha$ = 0.01  

p = 0.1237 ≥ 0.01

Do not reject H_0. There is insufficient evidence to conclude that  $\mu$ < 45

b) $\bar x$ = 43

s = 4.7

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (43-45) /4.7 / $\sqrt$ 36

= -2.553

P(z <-2.553 ) = 0.0076

P-value = 0.0076

$\alpha$ = 0.01  

p = 0.0076 < 0.01

Reject H_0. There is sufficient evidence to conclude that  $\mu$ < 45

C)

$\bar x$ = 46

s = 5

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (46-45) /5 / $\sqrt$ 36

= 1.2

P(z > 1.2) = 1 -  P(z <1.2 ) = 0.0076

P-value = 0.0076

$\alpha$ = 0.01  

p = 0.8809 ≥ 0.01

Do not reject H_0. There is insufficient evidence to conclude that  $\mu$ < 45