Question

a) We perform the Shapi f this ro-Wilk normality test to gather more information. The output o Shapiro-Wilk W test for normal dataProb>Z test is given below variable Obs 53 0.98 0.88 0.270.61 What is the p-value of this test? What is the conclusion? (3 credits) b) Assume that the distribution of the pH level is normal with ơ.1.20. Test H.: μ-7 versus H. : μ * 7 using a two-tailed test (significance level 0.01), (4 credits) Assume that the distribution of the pH level is normal with ơ-1.20. Test M) :f c) < 7 using a one-tailed test (significance level 0.01). (3 credits) -7 versus //" :f

Answer 1

SolutionA:

For shapiro.test

Ho:data follows normal distribution

Ha:data deviates from normal distribution

p=0.61

p>0.05

Fail to reject Ho.

Accept Ho,

Data follows normal distribution.

SolutionB:

Ho:mu=7

Ha:mu not =7

alpha=0.01

z=xbar-mu/sigma/sqrt(n)

=(6.59-7)/(1.20/sqrt(53)

z=-2.4874

p value in excel is

left tail prob =NORMSDIST(-2.487)=0.00644127

p=2*left tail prob=2*0.00644127=0.0129

that is p=0.0129

p>0.01

Fail to reject Ho.

Accept Ho.

Jims claim is correct that ph=7

Solutionc:

z stat

z=-2.4874

p value in excel is

left tail prob =NORMSDIST(-2.487)

p=left tail prob=0.00644127

alpha=0.01

p<0.01

Reject Ho.

Accept Ha.
Conclusion:

there is sufficient evidence at 1% level of significance to conclude that solutions are acidic as ph<7