Question

A publisher reports that 46% of their readers own a Jaguar. A marketing executive wants to test the claim that the percentage is actually more than the reported percentage. A random sample of 220 readers found that 50% of the readers owned a Jaguar. Is there sufficient evidence at the 0.05 level of significance to support the executive’s claim?

Determine the critical value from the chart. Explain what chart you used and how you found the value.

Determine the test statistic from your calculator. Explain what test you used in the calculator and the information you entered into the calculator.

What is the correct conclusion to this test? Explain your reasoning by comparing your test statistic to your critical value.

What is the conclusion in context?

Answer 1

Null hypothesis : The proportion of readers that own a Jaguar is 46%

P = 0.46

Alternative hypothesis : The proportion of readers that own a Jaguar is more than 46%

P > 0.46

Test statistic is given by -

Where, Po is the specified value of Population proportion under the null hypothesis = 0.46

Sample size = n = 220

Sample proportion = p = 50% = 0.50

So, the value of the test statistic will be -

  

= 1.18

Level of significance = 0.05

Now, the critical value of z at 0.05 level of significance for one tailed test = 1.645

It can be obtained using the z table by finding the z corresponding to the area close to 0.05. It will be at -1.6 and probability somewhere between 0.04 and 0.05. Hence, the critical value = 1.645 ( positive sign is because it is right tailed test)

Now, since, the critical value of z > value of the test statistic (it falls under the acceptance region), we may not reject the null hypothesis, hence, the proportion of readers owning a Jaguar is 0.46.

Hence, we don't have sufficient evidence to support the executive claim.