Answer:
(a) No, the coffee industry's claim is not supported by this sample.
(b) Null hypothesis: The average adult drinks 1.7 cups of coffee per day.
Alternate hypothesis: The average adult drinks more than 1.7 cups of coffee per day.
Step-by-step explanation:
(a) Test statistic (z) = (sample mean - population mean) ÷ sd/√n
sample mean = 1.9 cups per day
population mean = 1.7 cups per day
sd = 0.6 cups per day
n = 40
z = (1.9 - 1.7) ÷ 0.6/√40 = 0.2 ÷ 0.095 = 2.11
The test is a one-tailed test. Using alpha (significance level) = 0.1, the critical value is 2.326.
Conclusion:
Reject the null hypothesis because the test statistic 2.11 falls within the rejection region of the critical value 2.326.
The coffee industry's claim is contained in the null hypothesis, hence it is not supported by the sample because the null hypothesis is rejected.
(b) A null hypothesis is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.
An alternate hypothesis is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.
.