9. Hypothesis Testing for One Sample

Test the claim about the population mean $\mu$ at the given level of significance. Assume the population is normally distributed. Find the $P$-value and determine whether you should reject or fail to reject the null hypothesis.

Claim: $\mu \ne 1020$, $\alpha =0.01$, $\sigma =85$

Sample: $\bar{x}=990$, $n=40$

A university claims that the average SAT math score of its incoming freshmen is 600. A skeptical education researcher believes this might not be accurate. The researcher collects a random sample of 40 students and finds a sample mean SAT math score of 622. The population standard deviation is known to be 70. Using a significance level of $\alpha$ = 0.05, test the researcher’s claim.

Test the claim about the population mean $\mu$ at the given level of significance. Assume the population is normally distributed. Find the $P$-value and determine whether you should reject or fail to reject the null hypothesis.

Claim: $\mu >52$, $\alpha =0.10$

Sample: $\bar{x}=53.1$, $s=4.7$, $n=20$

A nutritionist believes the average daily protein intake for adults is $50g$. A random sample of $37$ adults has a sample mean of $51g$ sample standard deviation of $6g$. Use $\alpha =0.05$ to test whether the true mean protein intake differs from $50$ grams.