Question

According to the Centers for Disease Control, the mean number of cigarettes smoked per day by individuals who are daily smokers is 18.1. A researcher claims that retired adults smoke less than the general population of daily smokers. To test this claim, she obtains a random sample of 25 retired adults who are current smokers, and records the number of cigarettes smoked on a randomly selected day. The data result in a sample mean of 16.8 cigarettes and a standard deviation of 4.8 cigarettes. Do the data support the claim that retired adults who are daily smokers smoke less than the general population of daily smokers? Conduct a hypothesis test at α = 0.10. Assume the population is normally distributed. Hint: σ is unknown, and this is a one-tailed test. (5 points) State the hypotheses 〖 H〗_0: H_1: b. Compute test statistic (Round to the nearest 100th) c. Find critical value (Round to the nearest 100th) d. State decision rule: e. State your conclusion. First, state either “Reject the null hypothesis” or “Fail to reject it.” Then, interpret your conclusion:

Answer 1

a. Here claim is that retired adults who are daily smokers smoke less than the general population of daily smokers

So hypothesis is vs

b. As it is normal distribution but sigma is not known, we will use t distribution

c. The t-critical value for a left-tailed test, for a significance level of α=0.10 is

tc​=−1.32

Graphically

d. If test statistics falls in the rejection region, reject the null hypothesis

e. Here we see that test statistics falls in the rejection region so we reject the null hypothesis

We have sufficient evidence to support the claim that retired adults who are daily smokers smoke less than the general population of daily smokers