Question

We are interested in estimating the mean amount of rain last month in our county. It is known that the population standard deviation is 1.5 inches generally for the month of interest. 49 instruments that measure rainfall were placed throughout the county randomly. The sample mean from the instruments was 5.2 inches. Calculate a 95% confidence interval for the population mean of rainfall last month in the county. [Reference: Table A: Standard Normal Probabilities]

		4.78 to 5.62
		4.85 to 5.55
		4.93 to 5.47
		5.14 to 5.26

The 95% confidence interval for the population mean was calculated based on a random sample of size n=100n=100 as 5555 to 6565. What was the sample mean? Hint: Take a look at the formula for the confidence interval.

		5555
		57.557.5
		6060
		61.761.7
		62.562.5

The 95%95% confidence interval for the population mean was calculated based on a random sample of size n=100n=100 as 5555 to 6565. Does our confidence interval contain the true population mean?

		Yes.
		No.
		Maybe. Approximately 95%95% of the time, our 95%95% confidence interval will contain the true value of the parameter.

The 95%95% confidence interval for the population mean was calculated based on a random sample of size n=100n=100 as 5555 to 6565. What does this confidence interval tell us about the outcome of a 2-sided alpha = 0.05 test based on the null hypothesis ofH0:μ=57H0:μ=57?

		We would reject the null hypothesis of H0:μ=57H0:μ=57
		We would accept the null hypothesis of H0:μ=57H0:μ=57
		We would fail to reject the null hypothesis of H0:μ=57H0:μ=57
		Not enough information to decide,

Answer 1

1)

95% CI =4.78 to 5.62

2)

sample mean =(65+55)/2=60

3)

Maybe. Approximately 95% of the time, our 95% confidence interval will contain the true value of the parameter.

4)

We would fail to reject the null hypothesis of H0:μ=57