The Quartz Emporium, a local neighborhood supermarket, claims that they are the cheapest supermarket in town. The basis of their claim is from their aggregate 2019 sales data, in which they calculated that the mean amount of money spent per shopping trip to their store was $22.50, the least mean amount spent per shopping trip among all supermarkets in town. A local consumer advocacy group, the WatchDogs, suspects that Quartz Emporium has discreetly hiked up their prices. However, they are still touting the $22.50 mean amount spent per trip in order to attract shoppers. To get evidence, the WatchDogs sent pollsters to the Quartz Emporium to randomly survey 50 shoppers and recorded the amount they spent. Let μ represent the current mean amount spent per trip to their store.
Using the data provided, answer the following questions and provide the requested analysis

1) How should the WatchDogs frame their case in terms of a hypothesis testing problem? Specifically, what should be the null hypothesis and why? What should be the alternative hypothesis and why? – 1 pt
2) Assuming the amounts spent by the 50 randomly sampled shoppers is an iid sample from some Normal Distribution, what is the value of the standardized test statistic based on the data they collected? – 2 pts
3) As a claim of false advertising is a serious accusation, the WatchDogs want to be 90% certain they do not make such a claim in err. With the prior consideration in mind, what should the value of the standardized test statistic be before they are comfortable making the accusation of false advertising? – 1 pt
4) Based on the answers in part 2 and 3, what decision will the WatchDogs come to? – ½ pt
5) The Quartz Emporium learns that they are being investigated by the WatchDogs and warns them that they will not hesitate to sue if the group makes a false claim. Consequently, the WatchDogs decide instead to be 95% certain they do not make such a claim in err. Now what should the value of the standardized test statistic be before they are comfortable making the accusation of false advertising? – 1 pt
6) Based on the answers in part 2 and 5, what decision will the WatchDogs come to? – ½ pt

Spending
2.32
6.61
6.9
8.04
9.45
10.26
11.34
11.63
12.66
12.95
13.67
13.72
14.35
14.52
14.55
15.01
15.33
16.55
17.15
18.22
18.3
18.71
19.54
19.55
20.58
20.89
20.91
21.13
23.85
26.04
27.07
28.76
29.15
30.54
31.99
32.82
33.26
33.8
34.76
36.22
37.52
39.28
40.8
43.97
45.58
52.36
61.57
63.85
64.3
69.49