Question

1. An inventor has developed a new, energy-efficient lawn mower engine and claims that the engine will run continuously at least 300 minutes on a single gallon of regular gasoline. From his stock of 2000 engines, the inventor selects a simple random sample of 15 engines for testing. The engines run for an average of 305 minutes, with a sample standard deviation of 20 minutes. To test the inventors claim we use: Question 1 options:

	Two sided Z- test
	One sided chi-square test
	Two sided chi-square test
	Two sided T- test
	One sided T- test
	One sided Z- test

2. US department of labor wanted to compare the average unemployment rate in two different states California and Washington. From California they took a sample of size 25 and found that sample mean 20.32 and sample standard deviation is 3.55. From Washington they took a sample of size 45 and found that sample mean 21.24 and sample standard deviation is 2.70. Calculate the pooled variance.

3.

Following data shows number of ICU admission (X) and number of death per day (Y) for seven days due to COVID-19 virus. Fit a regression model of number of death per day (Y) on number of ICU admission (X) and estimate the number of death when ICU admission is 44.

Day	ICU admission (X)	Death (Y)
1	21	2
2	15	5
3	26	6
4	30	12
5	35	15
6	25	9
7	40	18
Total	192	67

4. A company has 500 part time workers. The company claims the variance is greater than 3.9 to test this claim a sample of 20 workers showed average of $ 18.70 per hours with sample variance 4.41. Calculate the test value  

5. A company has 500 part time workers. The company claims the variance is greater than 3.9 to test this claim a sample of 20 workers showed average of $ 18.70 per hours with sample variance 4.41. Calculate the critical value to test this claim when alpha=5%. (use chi-square table).

Answer 1