To test H0: = 80 versus H1: < 80. a simple random sample of size n = 22 is obtained from a population that is known to be normally distributed.
a) If ¯x = 76.9 and s = 8.5, compute the test statistic.
1.711
To compute the test statistic in this scenario, we need to use the sample mean (¯x), the sample standard deviation (s), and the sample size (n).
The test statistic we will use is the t-test statistic, which is calculated using the formula:
t = (¯x - μ) / (s / √n)
where ¯x is the sample mean, μ is the population mean (in this case, it is given as 80), s is the sample standard deviation, and n is the sample size.
Let's substitute the given values into the formula:
t = (76.9 - 80) / (8.5 / √22)
Calculating the value of the test statistic:
t = (-3.1) / (8.5 / √22)
Now, we simplify the expression inside the square root:
t = (-3.1) / (8.5 / 4.69)
Dividing:
t ≈ -3.1 / 1.81
Finally, we calculate the test statistic:
t ≈ -1.71
So, the test statistic is approximately -1.71.