Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.
-A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 700 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. Test whether the supplier's claim that no more than 1% are defective is supported or not supported.
A)not supported
B)supported

Question

Quizplus · Accepted Answer

The null hypothesis (H0) is that the proportion of defective disks is no more than 1% (p ≤ 0.01), and the alternative hypothesis (H1) is that the proportion of defective disks is more than 1% (p > 0.01). With a sample proportion of 3% defective disks out of 700, we calculate the test statistic using the formula for a proportion z-test: z = (p̂ - p0) / sqrt(p0(1-p0)/n), where p̂ is the sample proportion, p0 is the hypothesized population proportion, and n is the sample size. Substituting the values, we get z = (0.03 - 0.01) / sqrt(0.01(1-0.01)/700) = 0.02 / sqrt(0.01*0.99/700) ≈ 5.29. Comparing this z-value to the critical value for a 0.05 significance level in a one-tailed test (approximately 1.645), we find that the z-value is significantly higher, indicating that we reject the null hypothesis. Therefore, the claim that no more than 1% of the disks are defective is not supported.

Conduct a Full Hypothesis Test and Determine If the Given