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.