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
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.What is the value of the test statistic? Group of answer choicest = 1.26t = 1.65t = 1,8t = 1.50
Solution
To calculate the test statistic, we use the formula for a one-sample t-test:
t = (X̄ - μ) / (s/√n)
where: X̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
In this case: X̄ = 200 pounds, μ = 185 pounds, s = 59.5 pounds, and n = 25.
Substituting these values into the formula, we get:
t = (200 - 185) / (59.5/√25) = 15 / (59.5/5) = 15 / 11.9 = 1.26
So, the value of the test statistic is t = 1.26.
Similar Questions
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