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Answer :
Final answer:
The problem is a statistical one involving hypothesis testing. We first set up null and alternative hypotheses. After calculating the sample median and using it as our test statistic, we look at the p-value in relation to the significance level to determine if we have enough evidence to reject the null hypothesis. However, the sample size is small, and we take for granted that the sampled population follows a normal distribution, which may not be accurate.
Explanation:
The given question addresses a concept in statistics called hypothesis testing. To answer this question, we should first lay out our null and alternative hypotheses:
Null Hypothesis (H0): The median age of U.S. residents has not changed from 2007 and is still 36.6.
Alternative Hypothesis (Ha): The median age of U.S. residents has increased from 2007 and is more than 36.6.
Now we calculate the median age from the given sample of 10 U.S. residents, which comes out to be 43.5 years. The alternative hypothesis asserts that the median age is above 36.6 years, hence it's a one tailed test.
The test statistic in this case would be the difference between the sample median (43.5) and the population median (36.6). To decide whether the observed value of the test statistic is unlikely, under the assumption that the null hypothesis is true, we compare the p-value with the significance level (1%).
If the p-value is less than the significance level, the result is termed statistically significant, and you reject the null hypothesis i.e., it's safe to conclude that the median age has increased. On the other hand, if the p-value is greater, then you fail to reject the null hypothesis and it's assumed there isn't enough evidence to conclude the median age has increased.
However, it should be noted that this test is based on the assumption that the sampled population follows a normal distribution which is not mentioned in the question. Also, it's based on a small random sample which may not accurately represent the entire population.
Learn more about Hypothesis Testing here:
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