7.3 Hypothesis testing for the mean (sigma unknown)
Use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ >78; α=0.01 Sample statistics: x bar=80.7, s=3.6, n=28 Null and alternate hypotheses?
H0: mu < or equal to 78 Ha: mu > 78 standardized test statistic? 3.97 (x bar- mu)/(s/sqrt of n) p-value= 0.000 Reject H0- there is enough evidence to support the claim p-value= STAT--> TESTS, t-test, fill in info (mu NULL) not always the same as mu)
Find the critical value(s) using the t-distribution table in the row with the correct degrees of freedom.
If the hypothesis test is left-tailed, use the *One Tail, alpha* column with a *negative* sign right-tailed- use the *one tail, alpha* column with a *positive* sign two-tailed- *two tails, alpha* column with a *negative and positive* sign
Explain how to find the critical values for a t-distribution.
The first step is to identify the level of significance alphaα and the degrees of freedom, d.f.=n−1.
State whether the standardized test statistic t indicates that you should reject the null hypothesis. (a) t=1.752 (b) t=0 (c) t=1.625 (d) t= -1.758 (R-tailed, Z0= 1.666)
a) reject, cuz t > b) fail to reject cuz t < c) Fail to reject cuz t < D)fail to reject cuz t < 1.666
Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. Left-tailed test, α=0.005, n=15
critical value= -2.977 rejection region= t< -2.977 (left of, less than)
Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. right-tailed test, α=0.05, n=22
critical value= 1.721 (using t-distribution table) Determine the rejection region(s)= t > 1.721
Use a t-test to test the claim about the population mean muμ at the given level of significance alphaα using the given sample statistics. Assume the population is normally distributed. Claim: μ≠28; α=0.05 Sample statistics: xbar=26.2, s=4.9, n=11 If the P-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
null and alternate hypotheses? H0: mu = 28 Ha: mu NOT= 28 standardized test stat? -1.22 p-value= 0.251 Fail to refect H0. Not enough evidence to support claim.
