Question

Lola is using a one-sample t-t- test for a population mean, µμ , to test the null hypothesis, H0:µ=40 mg/dLH0:μ=40 mg/dL , against the alternative hypothesis, H1:µ>40 mg/dLH1:μ>40 mg/dL . Her results are based on a simple random sample of size n=15 . The value of the one-sample t-t- statistic is t=1.457 .
If Lola requires her results to be statistically significant at significance level of a 0.10, what can she conclude and why?

a. Because the exact p-value is unknown, she cannot make a conclusion.
b. She should not reject the null hypothesis because p > 0.10.
c. She should not reject the null hypothesis because p< 0.10.
d. She should reject the null hypothesis because p< 0.10,
e. She should not reject the null hypothesis because 0.10< p < 0.05.

Answer 1

Answer:

d. She should reject the null hypothesis because p < 0.10.

Step-by-step explanation:

We have a t statistic, so let's solve for the P-value on our calculators. (tcdf on a TI-84 calculator is 2nd->VARS->6.)

tcdf(left bound, right bound, degrees of freedom)

• Our left bound is t=1.457.

• Our right bound is infinity, because we're interested in the hypothesis µ>40 mg/dL. We use 999 to represent infinity in the calculator.
• Our degrees of freedom is n-1 = 15-1 = 14.

tcdf(1.457,999,14) = .084

.084 < P-value of .10, so we reject the null hypothesis.