You will be using StatKey to conduct randomization tests for a single proportion

Question

You will be using StatKey to conduct randomization tests for a single proportion. For each test take at least 6,000 samples. The library is planning its orders for the next year and wants to know if more than 60% of all stat 460 students students want to purchase a hardback copy of the mcgrawhill textbook.

Using the five steps from the online notes, conduct a randomization test given that 14 students in a random sample of 20 want to purchase a loose-leaf copy of the textbook. Be sure to include your relevant StatKey output.

Step 1: Determine what type of test you need to conduct and write the hypotheses.

Step 2: Construct a randomization distribution under the assumption that the null hypothesis is true.

Step 3: Use the randomization distribution to find the p-value.

Step 4: Decide if you should reject or fail to reject the null hypothesis.

Step 5: State a real-world conclusion in relation to the original research question.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.60
Alternative hypothesis: P > 0.60

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.109545
z = (p - P) /

z = 0.913

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 0.913.

Thus, the P-value = 0.1815

Interpret results. Since the P-value (0.1815) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that more than 60% of all stat 460 students students want to purchase a hardback copy of the mcgrawhill textbook.

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