(Solved): 4. The average American gets a haircut every 38 days. Is the average smaller for college students? T ...

The average American gets a haircut every 38 days. Is the average smaller for college students? The data delow shows the results of a survey of 16 college students asking them how many days elapse between naircuts. Assume that the distribution of the population is normal. \[ 35,27,36,37,39,37,41,29,32,26,28,41,38,42,27,33 \] What can be concluded at the the \( \alpha=0.01 \) level of significance level of significance? a. For this study, we should use b. The null and alternative hypotheses would be: \( \mathrm{H}_{0} \) : \( H_{1} \) : c. The test statistic \( \quad=\quad \) (please show your answer to 3 decimal places.) d. The \( p \)-value \( =\quad \) (Please show your answer to 3 decimal places.) e. The p-value is \( \alpha \) f. Based on this, we should g. Thus, the final conclusion is that ... the null hypothesis. The data suggest the populaton mean is significantly lower than 38 at \( \alpha=0.01 \), so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 38 . The data suggest the population mean is not significantly lower than 38 at \( \alpha=0.01 \), so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 38. The data suggest the population mean number of days between haircuts for college students is not significantly lower than 38 at \( \alpha=0.01 \), so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 38 .