An investigator wants to assess whether the mean (mu) = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 25 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. Which of the following is an appropriate conclusion (alpha= .05)? Group of answer choicesthe average total weight of all passengers appears to be greater than 185 pounds.null hypothesis should be revisedthe average total weight of all passengers appears to be not greater than 185 pounds.
Question
An investigator wants to assess whether the mean (mu) = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 25 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. Which of the following is an appropriate conclusion (alpha= .05)? Group of answer choicesthe average total weight of all passengers appears to be greater than 185 pounds.null hypothesis should be revisedthe average total weight of all passengers appears to be not greater than 185 pounds.
Solution
To answer this question, we need to conduct a one-sample t-test to test the hypothesis that the mean weight of passengers exceeds 185 pounds.
Step 1: State the hypotheses. The null hypothesis is that the mean weight is 185 pounds. The alternative hypothesis is that the mean weight is greater than 185 pounds.
Step 2: Calculate the test statistic. The formula for the test statistic in a one-sample t-test is (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Plugging in the given values, we get (200 - 185) / (59.5 / sqrt(25)) = 1.27.
Step 3: Determine the critical value. For a one-tailed test with alpha = 0.05 and degrees of freedom = 24 (sample size - 1), the critical value from the t-distribution table is approximately 1.711.
Step 4: Make the decision. Since the test statistic (1.27) is less than the critical value (1.711), we do not reject the null hypothesis.
Therefore, the appropriate conclusion is that the average total weight of all passengers appears to not be greater than 185 pounds.
Similar Questions
An investigator wants to assess whether the mean (mu) = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 25 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed.What is the value of the test statistic? Group of answer choicest = 1.26t = 1.65t = 1,8t = 1.50
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