Question

The average American gets a haircut every 40 days. Is the average different for college students? The data below shows the results of a survey of 16 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal.

40, 40, 46, 40, 31, 46, 34, 44, 34, 42, 36, 27, 37, 46, 40, 37

What can be concluded at the the α α = 0.10 level of significance level of significance?

1. For this study, we should use (z-test for a population proportion, t-test for a population mean )
2. The null and alternative hypotheses would be:

H0: ( p, μ) (?, ≠, <, >, =)   

H1: ( p, μ) (?, <, =, >, ≠)

3. The test statistic ( t,z) =________ (please show your answer to 3 decimal places.)
4. The p-value = _________(Please show your answer to 3 decimal places.)
5. The p-value is ( ≤, >) α
6. Based on this, we should ( accept, reject, fail) to reject the null hypothesis.
7. Thus, the final conclusion is that ...

*The data suggest the populaton mean is significantly different from 40 at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 40.

*The data suggest the population mean is not significantly different from 40 at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 40.

*The data suggest the population mean number of days between haircuts for college students is not significantly different from 40 at αα = 0.10, so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 40.

Answer 1