The owner of an apricot orchard wants to find out if the yield per tree will be 51kg this season. He takes a random sample of 70 trees and records the yield for each tree. This results in a sample mean of 69.3kg with a sample standard deviation of 9kg.He consults a friendly statistician who carries out a one-sample t-test.Give the test statistic to 2 decimal places Answer
Question
The owner of an apricot orchard wants to find out if the yield per tree will be 51kg this season. He takes a random sample of 70 trees and records the yield for each tree. This results in a sample mean of 69.3kg with a sample standard deviation of 9kg.He consults a friendly statistician who carries out a one-sample t-test.Give the test statistic to 2 decimal places Answer
Solution
To calculate the test statistic for a one-sample t-test, we use the formula:
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 = 69.3kg (the sample mean) μ = 51kg (the population mean we are testing against) s = 9kg (the sample standard deviation) n = 70 (the sample size)
Substituting these values into the formula gives:
t = (69.3 - 51) / (9/√70)
Calculating the denominator first:
9/√70 = 1.076
Then substitute this into the formula:
t = (69.3 - 51) / 1.076
t = 18.3 / 1.076
t = 17.00
So, the test statistic (t) is 17.00 to 2 decimal places.
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