Suppose you instead wish to calculate a 90% confidence interval for the population for the population mean using the same sample data. Which of the following intervals could be the 90% confidence interval?
a. (23,37)
b. (24, 36)
c. (24, 34)
d. (25, 35)
The correct answer is c. (24, 34).
A 90% confidence interval means that we are 90% confident that the true population mean falls within the interval. To calculate this interval, we need to take into account the sample mean and the standard error.
From the sample data, let's say the sample mean is x̄ and the standard deviation is s (or we can use the sample standard error, which is s/√n, where n is the sample size).
Since we want a 90% confidence interval, we need to find the z-score corresponding to that confidence level. The z-score at a 90% confidence level is approximately 1.645.
Now we can calculate the interval using the formula:
Interval = x̄ ± (z * standard error)
where z is the z-score and standard error = s/√n.
Without the exact values of the sample mean, standard deviation, and sample size, we cannot calculate the interval precisely. However, based on the given options, the interval (24, 34) is most likely to be the correct answer since it is the closest to the calculated interval with a 90% confidence level.