Final answer:
For the average age of customers who buy a BMX bicycle being 47 or less, a t-test gives us a p-value of 0.03. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis, indicating that there is sufficient evidence to conclude that the average age is indeed 47 or less.
Step-by-step explanation:
To answer the question, we must complete a statistical test using the t-test to see if the average age of customers who buy a BMX bicycle is 47 or less. With an alpha level (α) of 0.05, we compare the p-value of the test to this significance level. If the p-value is less than 0.05, we reject the null hypothesis, which states that the average age is greater than or equal to 47. The options given are:
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- a) P-value = 0.03; Reject the null hypothesis
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- b) P-value = 0.10; Reject the null hypothesis
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- c) P-value = 0.03; Do not reject the null hypothesis
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- d) P-value = 0.10; Do not reject the null hypothesis
Using the given options and the information above, we select the correct answer. Since option (a) states that the p-value is 0.03, which is less than the significance level of 0.05, we would reject the null hypothesis. Thus, option (a): P-value = 0.03; Reject the null hypothesis is the correct answer.
On the other hand, if the p-value had been higher than 0.05, like in options (b) and (d), we would not have enough evidence to reject the null hypothesis and would thereby not reject it.
Conclusion:
The test indicates there is sufficient evidence at the 5% significance level to conclude that the average age of customers who buy a BMX bicycle is less than or equal to 47 years. Thus, we reject the null hypothesis.