Question

By sampling 100 pennies, students will test the validity of a hypothesis they have made about the age of all pennies. 90% of the pennies are older than 10 years. Points for the project as follows: (5 points) Correctly state the hypotheses and claim (5 points) Determine the critical value (5 points) Determine the proportion of pennies by age of the sample (10 points) Accept or Reject the null hypothesis and determine if the claim is supported.

Answer 1

Since you have not provided how many pennies will be older than 10 years out of 100 pennies

I am assuming it to be X = 95

you can change this number if you want

Ho : p = 0.9

Ha : p 0.9

assuming alpha = 0.05

critical value = 1.96

p^ = X/n = 95/100 = 0.95

TS = (p^ - p)/sqrt(pq/n)

= (0.95 - 0.9)/sqrt(0.9*0.1/100)

= 1.6667

for two-tailed test

when |TS| > critical value

we reject the null hypothesis

since TS = 1.6667 < 1.96 critical value

we fail to reject the null hypothesis

There is not sufficient evidence to reject the claim