The owner of a local restaurant wants to estimate the number of orders received per day. To that end, they record the number of orders on 120 days randomly picked across six months. The average number of orders over those 120 days was 70 and the standard deviation was 15.
(4 pts) Compute a 95% confidence interval for the population parameter of the number of daily orders. What is the margin of error? (Use 1 decimal place)
1 pt) Identify as true or false: On 95% of the days during any six months, the restaurant receives orders ranging from the upper and lower bound that you calculated in part 1.
(5 pts) Suppose the restaurant owner now wants a 99% confidence interval for the number of daily orders with the same sample of 120 days (average: 70 and standard deviation: 15). Compute the 99% confidence interval. How do the margin of error and the confidence interval change in comparison to those for the 95% case? Show your work. (Use 1 decimal place.)
(5 pts) The owner of the restaurant is now interested in the proportion of days in a six-month period on which they receive 60 or higher number of orders. The count of such days, out of the 120 days they selected earlier, was 95. Compute the proportion of days that receive 60 or higher number of orders. Compute a 95% confidence interval for the proportion of days on which they received 60 or more orders. What is the margin of error? Show your work. (Use 2 decimal places)
(2 pts) Suppose after a year of the study, the owner feels that the restaurant has become more popular and hence anticipates the daily order to have increased from 70 to 90. The owner wants to conduct a hypothesis test to see if there is evidence that the daily order is now 90 where what is expected is that it is still 70. Identify the null hypothesis and the alternative hypothesis.
(2 pts) To verify the new claim, you conduct a random sampling and gather new data. The p-value turns out to be 0.02. With respect to the significance level of 0.05, what would be your decision? Is the new data statistically significant or simply due to random chance?