Question

Consider the hypotheses shown below. Given that

x overbarxequals=57​,

sigmaσequals=12​,

nequals=37​,

alphaαequals=0.10​,

complete parts a and b.

Upper H 0H0​:

muμless than or equals≤55

Upper H 1H1​:

muμgreater than>55

​a) The​ z-test statistic is?

(Round to two decimal places as​ needed.)

b)The critical​ z-score(s) is(are) ?

(Round to two decimal places as​ needed.)

C)Reject or fail to reject, why or why not?

D)p-value?

(Round to four decimal places as​ needed.)

Answer 1

Solution :

= 55

= 57

= 12

n = 37

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   ≤ 55

H_a : >  55

Test statistic is z

z = ( - ) / / n

= (57-55) /12 / 37

= 1.01

Test statistic z = 1.01

P(z > 1.01 ) = 1 - P(z < 1.01 ) = 1 - 0.1562

P-value = 0.1562

= 0.10  

b )The critical​ z-score

The significance level is α = 0.10, and the critical value for a right-tailed test is z_c​= 1.28

it is observed that z = 1.014 ≤ z_c ​=1.28, it is then concluded that the null hypothesis is not rejected

c ) It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean \muμ is greater than 55, at the 0.10 significance level It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is greater than 55, at the 0.10 significance level

d ) P(z > 1.01 ) = 1 - P(z < 1.01 ) = 1 - 0.1562

P-value = 0.1562