Question

4. Price scanners at O-mart are supposed to produce no more than 2% errors. Īs this under-stated? We randomly sample n-1000 scans and find z = 28 of the scans produce an incorrect price. Use significance level a 0.05 (a) (5 points) State the null and alternative hypothesis. (b (5 points) Show that the conditions for the assumption of normality hold. (c) (5 points) Calculate the valuc of the test statistic. Show your workings. Value of test statistic d) (5 points) Find the critical value associated with this test Critical value (e) (5 points) Based on the critical value, the decision is: (circle one) Reject Ho/ Not reject Ho Conclusion:

Show work please.

Answer 1

a)

H0 : p = 0.02
Ha: p < 0.02

b)

The sample must be reasonably random.
• The data must be from a normal distribution or large sample (need to check n ≥ 30 ).
• σ must be known.
• The sample must be less than 10% of the population so that sigma/sqrt(n)) is valid for the standard deviation of the sampling distribution of xbar

c)
phat = 28/1000 = 0.028

z = (phat - p)/sqrt(p*(1-p)/n)
= (0.028 - 0.02)/sqrt(0.02*(1-0.02)/1000) .
= 1.81

d)

Critical value = -1.645

e)

zstat < -1.645
Do not reject H0