1)Â Â Â Â Â Â Â Â The populationstandard deviation for waiting times to be seated at a restaurantis known to be 10 minutes. An expensive restaurant claims that theaverage waiting time for dinner is approximately 1 hour, but wesuspect that this claim is inflated to make the restaurant appearmore exclusive and successful. A random sample of 30 customersyielded a sample average waiting time of 50 minutes.
- Is there evidence to say that the restaurant’s claim is toohigh? Insert the results from StatCrunch here.
- State the hypotheses, your decision and conclusion. Include thereason for your decision using the output from above.
- The original data (individual waiting times) is not normallydistributed. What theorem allows us to do the calculations in part(a)?
2)Â Â Â Â Â Â Â Â A sample of 800items produced on a new machine showed that 48 of them aredefective. The factory will get rid the machine if the dataindicates that the proportion of defective items is significantlymore than 5%. At a significance level of 10% does the factory getrid of the machine or not?
- Insert the results from StatCrunch here.
- State the hypotheses, your decision and conclusion. Include thereason for your decision using the results from above.
3)Â Â Â Â Â Â Â Â A psychologistclaims that the mean age at which children start walking is 12.5months. The following data give the age at which 18 randomlyselected children started walking.
15 Â Â Â Â Â Â 11Â Â Â Â Â Â 13Â Â Â Â Â Â 14Â Â Â Â Â Â 15Â Â Â Â Â Â 12Â Â Â Â Â Â 15Â Â Â Â Â Â 10Â Â Â Â Â Â 16
17 Â Â Â Â Â Â 14Â Â Â Â Â Â 16Â Â Â Â Â Â 13Â Â Â Â Â Â 15Â Â Â Â Â Â 15Â Â Â Â Â Â 14Â Â Â Â Â Â 11Â Â Â Â Â Â 13
- Test at the 1% level of significance if the mean age at whichchildren start walking is different from 12.5 months. Insert theresults from StatCrunch here.
- State the hypotheses, state your decision and conclusion.Include the reason for your decision from the results above.
4)Â Â Â Â Â Â Â Â According to astudy, 107 of 507 female college students were on a diet at thetime of the study.
a) Construct a 99% confidence intervalfor the true proportion of all female students who were on a dietat the time of this study. Insert the results from StatCrunchhere.
b) Interpret this interval.
c) Is it reasonable to think that only 17% of college women areon a diet? Why or why not?
