Media Disk, Inc. duplicates over a million 3.5” floppy disks each year by copying masters to stacks of blank disks. The company buys its blank stock from two different suppliers, A and B. The manager has decided to check each supplier’s stock by counting the rejected disks in the next run from 5,000 that just arrived from supplier A and 4,500 that just arrived from supplier B. During the run, the disk duplicators rejected 73 of A’s disks and 56 of B’s. State the appropriate hypotheses to test whether the proportions of defective disks from the two suppliers are the same. At a = 0.05, what can Media Disk conclude? This question is due on day 6.
Try a binomial proportion 2-sample z-test using proportions.
Hypotheses:
Ho: pA = pB
Ha: pA does not equal pB -->this is a two-tailed test (the alternate hypothesis does not show a specific direction).
The formula is:
z = (pA - pB)/√[pq(1/n1 + 1/n2)]
...where n represents the sample sizes, p is (x1 + x2)/(n1 + n2), and q is 1-p.
I'll get you started:
p = (73 + 56)/(5000 + 4500) = ? -->once you have the fraction, convert to a decimal (decimals are easier to use in the formula).
q = 1 - p
pA = 73/5000
pB = 56/4500
Convert all fractions to decimals. Plug those decimal values into the formula and find z. Compare z to the cutoff 0.05 for a two-tailed test (cutoff value is z = + or - 1.96). If the test statistic you calculated exceeds either the positive or negative cutoff z-value, reject the null and conclude a difference. If the test statistic does not exceed either the positive or negative cutoff z-value, do not reject the null (you cannot conclude a difference).
I hope this will help get you started.
To test whether the proportions of defective disks from suppliers A and B are the same, we can use a hypothesis test. The null hypothesis (H0) assumes that the proportions are equal, while the alternative hypothesis (H1) assumes that they are not equal.
H0: The proportion of defective disks from supplier A is equal to the proportion of defective disks from supplier B.
H1: The proportion of defective disks from supplier A is not equal to the proportion of defective disks from supplier B.
To test these hypotheses, we can use a two-sample proportion test. Here is how you can perform the test:
1. Calculate the sample proportions of defective disks for each supplier:
- p̂A = Number of defective disks from supplier A / Total number of disks from supplier A
- p̂B = Number of defective disks from supplier B / Total number of disks from supplier B
2. Calculate the standard error (SE) of the difference in proportions:
- SE = sqrt(p̂A * (1 - p̂A) / nA + p̂B * (1 - p̂B) / nB)
3. Calculate the test statistic:
- Test statistic (Z) = (p̂A - p̂B) / SE
4. Determine the critical value(s) for the desired significance level (α) of 0.05. In this case, we can use a two-tailed test, so we divide α by 2. Look up the critical value(s) in the standard normal distribution table.
5. Compare the test statistic with the critical value(s). If the test statistic falls outside the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
6. Make a conclusion based on the test results. If the null hypothesis is rejected, it means there is sufficient evidence to conclude that the proportions of defective disks from the two suppliers are different. If the null hypothesis is not rejected, it means there is not enough evidence to conclude a difference in proportions.
Remember to calculate the appropriate sample proportions, standard error, and test statistic using the given data in order to make a conclusion.