Question

4. The FloridaLakes dataset describes characteristic of water samples taken at random Florida lakes. Acidity (pH) is given for each lake. Pure water has a pH of 7,which is neutral. with a pH less than 7 are acidic while solutions with a pH greater than 7 are basic or alkaline. A rcher Jim Lee would like to know whether on average the solutions in Florlida lakes are acidic. In order to test whether on average the solutions in Florida lakes are acidic, im Lee collected a random sample with 53 observed values. The mean of the sample is 659 Jim Lee claimed that the mean of the pH level in the population is 7.In order to test if Jim Lee's claim is correct, we perform hypothesis test. a) We perform the Shapiro-Wilk test is given below. normality test to gather more information. The output of this variable Shapiro Wilk w test for normal data obs 53 Prob>Z 0.61 0.98 -0.27 0.88 What is the p-value of this test? What is the conclusion? (3 cre dits) b) Assume that the distribution of the pH level is normal with σ 1.20. Test o7 versus H7 using a two-tailed test (significance level 0.01). (4 cred Assume that the distribution of the pH level is normal with o-1.20. Test Ho c) 7 versus H

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