A random sample of size 21 was taken from a normal population. The sample average was 9.87 and the sample SD was 1.17. What test should you use for testing whether the population mean equals 9.7?
Assume all samples are simple random samples and α (alpha) is taken to be 0.05.
To test whether the population mean equals 9.7, we can use a t-test since the population standard deviation is unknown.
Given that the sample size is 21, the sample mean is 9.87, and the sample standard deviation is 1.17, we can calculate the t-statistic as follows:
t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))
= (9.87 - 9.7) / (1.17 / sqrt(21))
= 0.17 / (1.17 / 4.582)
= 0.17 / 0.255
= 0.6667
With 20 degrees of freedom (sample size - 1), we can use a t-distribution table or software to find the critical value for α = 0.05. Looking up the value in the t-distribution table, we find that the critical value is approximately 2.086.
Since the absolute value of the calculated t-statistic (0.6667) is less than the critical value (2.086), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the population mean is different from 9.7 at the 0.05 significance level.