Null Hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is 45% or more.
Alternative Hypothesis (Ha): The proportion of newsletter readers who own a Rolls Royce is less than 45%.
To test the publisher's claim at the 0.01 significance level, we need to perform a one-tailed hypothesis test.
We would use a statistical test like the proportion z-test or the binomial test to compare the observed proportion of Rolls Royce owners with the proportion stated in the null hypothesis (45%).
Important Note: We cannot definitively prove or disprove a hypothesis, only reject or fail to reject it.
Therefore, if the p-value is less than 0.01, we would reject the null hypothesis and conclude that there is evidence to suggest that less than 45% of the readers own a Rolls Royce.
However, we cannot be 100% certain that this is the case.
Additional Information Needed:
To perform the test accurately, we need additional information:
Sample size: The number of newsletter readers surveyed.
Number of Rolls Royce owners: The number of readers who reported owning a Rolls Royce in the survey.
With this information, we can calculate the observed proportion of Rolls Royce owners and the p-value of the test. Based on the p-value, we can then draw conclusions about the publisher's claim.
Limitations:
It's important to consider the limitations of this analysis:
Sample bias: The sample may not be representative of the entire population of newsletter readers.
Self-reporting: Respondents may not accurately report their Rolls Royce ownership.
Other factors: The publisher's claim may be based on other factors, such as demographics or income, that are not considered in the test.
Therefore, while a hypothesis test can provide valuable insights, it's crucial to interpret the results with caution and consider the limitations of the data and methodology.
Question
A newsletter publisher believes that under 45% of their readers own a Rolls Royce.
Is there sufficient evidence at the 0.01 level to substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario.