Question

A random sample of tenth-grade boys resulted in the following 20 observed weights. 142,134,98,119,131,103,154,122, 93, 137, 86,119,161,144,158,165,81,117,128,103

a). Test the hypotheses that the median weight is 103 . Use the quantile test keeping the significance level at no more than 0.05. Give hypotheses, your decision rule, test statistic value, p-value, and conclusion.

Answer 1

To test the hypothesis that the median weight is 103, we can use the quantile test. The null hypothesis is that the median weight is equal to 103, and the alternative hypothesis is that the median weight is not equal to 103. We calculate the test statistic value, p-value, and make a decision based on the significance level.

Step-by-step explanation:

To test the hypothesis that the median weight is 103, we can use the quantile test. The null hypothesis (H0) is that the median weight is equal to 103, and the alternative hypothesis (Ha) is that the median weight is not equal to 103.
The p-value is calculated using the binomial distribution. The p-value is the probability of obtaining a test statistic value of 9 or less, given that the null hypothesis is true. Using a significance level of 0.05, we compare the p-value to the significance level. If the p-value is less than or equal to the significance level, we reject the null hypothesis. In this case, the p-value is 0.00016, which is less than 0.05, so we reject the null hypothesis.
Therefore, we conclude that there is sufficient evidence to suggest that the median weight is not equal to 103.