Question

Lead in Medicine Listed below are the lead concentrations (in μg/g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from "Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet," by Saper et al., Journal of the American Medical Association, Vol. 300, No. 8. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 μg/g.
3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5

Answer 1

Step-by-step explanation:

We start by calculating mean and standard deviation

Mean = sum of all values/total number of values

= 110.5/10

= 11.05

Standard deviation = √375.725/9

= √41.7472

= 6.46

Null hypothesis =

h0: μ = 14

Alternate hypothesis =

H1: μ < 14

Alpha is set at 0.05

Test statistic

T = mean - (μ)/(sd/√n)

=(11.05-14)/(6.46/√10)

= -2.95/2.0428

= -1.4441

P value calculator

df = n-1 = 10 -1 = 9

P Value = trust(x,df,tails)

= trust(1.4441,9,1)

= 0.0913

In conclusion our pvalue is greater than alpha level at 0.05 so we do not have sufficient evidence to reject the null hypothesis. We do not have enough evidence to accept the alternate so we reject claim that mean lead concentration for all such medicine is < than 14μg/g