Question

Consider the following hypothesis test. Ha: μ < 50 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use -0.01. X (a) 49 and s-5.2 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion. Do not reject Ho There is insufficient evidence to conclude that u 50 O Reject Ho. There is sufficient evidence to conclude that μ < 50. O Do not reject Ho. There is sufficient evidence to conclude that u < 50. O Reject Ho. There is insufficient evidence to conclude that μ < 50. (b) x = 48 and s = 4.5 Find the value of the test statistic. (Round your answer 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 insufficient evidence to conclude that μ < 50. O Reject Ho. There is sufficient evidence to conclude that μ < 50. O Do not reject Ho. There is sufficient evidence to conclude that μ < 50. O Reject Ho. There is insufficient evidence to conclude that μ < 50.

Answer 1

H0 : mu > =50
Ha: mu < 50

a)

t = (xbar - mu)/(s/sqrt(n))
= ( 49 -50)/(5.2/sqrt(36))
= -1.154

p value = 0.1282

As p value > 0.01

Do not reject H0 There is sinsufficient evdience to conclude that mu < 50

b)

t = (xbar - mu)/(s/sqrt(n))
= ( 48 -50)/(4.5/sqrt(36))
= -2.667

p value = 0.0058

As p value < 0.01

reject H0 There is sufficient evdience to conclude that mu < 50

c)

t = (xbar - mu)/(s/sqrt(n))
= ( 51 -50)/(4/sqrt(36))
= 1.500

p value = 0.9287

As p value > 0.01

Do not reject H0 There is sinsufficient evdience to conclude that mu < 50