We want to conduct a hypothesis test of the claim that the population mean score on a nationwide examination in anthropology is different from . So, we choose a random sample of exam scores

Question

We want to conduct a hypothesis test of the claim that the population mean score on a nationwide examination in anthropology is different from 

502

. So, we choose a random sample of exam scores. The sample has a mean of 520

 and a standard deviation of 76

.For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places.

	(a)	The sample has size 14	, and it is from a population with a distribution about which we know very little.
		=z
		=t
		It is unclear which test statistic to use.

Answer 1

Hi Equong,

Essentially, this is two questions in one; first, what type of hypothesis test you want to use: z or t? If the population standard deviation sigma is known, you can use z. If not, you need to use t. Here, we were given only a sample standard deviation (s) and told we know little about the population, so use t.

To compute the t-test statistic:

t = xbar -mu / SE, SE = standard error = s/sqrt(n)

xbar = sample mean = 520

mu = hypothesized mean = 502

s = sample st. dev. = 76

n = sample size = 14

SE = 76/sqrt(14) = 20.312

t = (520 - 502) / 20.312

t = 0.89

I hope this helps.