A local group of economists wants to study the effects of the pandemic on the small businesses in their city. A survey was sent out to a random sample of small businesses to anonymously report both their weekly earnings in $1000 for January 2020 (group 1) and January 2021 (group 2). Assume that the weekly earnings are normally distributed. Only 10 businesses provided enough data to compute their average weekly earnings for two months. The groups are dependent. Use α = 0.01 to decide whether there is sufficient evidence that the pandemic reduced the average weekly earnings for small businesses. January 2020 January 2021 58.2 60.5 78.3 62.5 38.2 40.9 32.7 36.2 43.8 36.2 33.7 30.9 50.5 41.4 56.3 38.3 41.1 37.9 26.4 21.7 1. What are the correct hypotheses? H0: H1: 2. Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The critical value is = 3. The decision is to The correct summary would be: that the pandemic reduced the average weekly earnings for small businesses.
A local group of economists wants to study the effects of the pandemic on the small businesses in their city. A survey was sent out to a random sample of small businesses to anonymously report both their weekly earnings in $1000 for January 2020 (group 1) and January 2021 (group 2). Assume that the weekly earnings are
Use α = 0.01 to decide whether there is sufficient evidence that the pandemic reduced the average weekly earnings for small businesses.
| January 2020 | January 2021 |
|---|---|
| 58.2 | 60.5 |
| 78.3 | 62.5 |
| 38.2 | 40.9 |
| 32.7 | 36.2 |
| 43.8 | 36.2 |
| 33.7 | 30.9 |
| 50.5 | 41.4 |
| 56.3 | 38.3 |
| 41.1 | 37.9 |
| 26.4 | 21.7 |
1. What are the correct hypotheses?
H0:
H1:
2. Based on the hypotheses, compute the following:
Round answers to at least 4 decimal places.
The test statistic is =
The critical value is =
3. The decision is to
The correct summary would be: that the pandemic reduced the average weekly earnings for small businesses.
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