PLease provide excel sheet if possible. If not, no worries..

Q1: Consider the following sample of six gasoline mileages: 32.3,30.5,31.7,31.6,31.4,32.6

Calculate the mean

Calculate the sample variance

Calculate the sample standard deviation

. Q2. Use the first 30 observations in the mileages data attached to solve for the measurements below. Explain what each measurement means and how decision-makers can use this information.

Calculate the sample mean

Calculate the sample variance

Calculate the sample standard deviation

Construct a histogram for the data

Q3. Suppose that the population of all gasoline mileages is normally distributed with mean = 31.5 mpg and standard deviation = 0.8 mpg. Let y denote a mileage randomly selected from this population. Find the probabilities:

P(30.7 y 32.3)

P(31.0 y 31.3)

P(y 29.5)

P(y 33.4)

Q4. Assume that the population of all mileages is normally distributed. Use the following sample of n = 5 mileages:

32.3,30.5,31.7,31.4,32.6 to find 95% and 99% confidence intervals (please make sure to show all of your work).

Q5. The bad debt ratio for a financial institution is defined to be the dollar values of loans defaulted divided by the total dollar values of all loans made. A random sample of seven Ohio banks is selected. The bad debt ratios for these banks are 7, 4, 6, 7, 5, 4, and 9%.

The mean bad debt ratio for all federally insured banks is 3.5%. Federal banking officials claim that the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks. Set up the null and alternative hypotheses that should be used to justify this claim statistically.

Assuming bad debt ratios for Ohio banks are normally distributed, use the sample results give above to test the hypotheses you set up in part (a) with a = .01. Interpret the outcome of the test.

Gasoline mileages

30.8

31.7

30.1

31.6

32.1

33.3

31.3

31

32

32.4

30.9

30.4

32.5

30.3

31.3

32.1

32.5

31.8

30.4

30.5

32

31.4

30.8

32.8

30.6

31.5

32.4

31

29.8

31.1

32.3

32.7

31.2

30.6

31.7

31.4

32.2

31.5

31.7

30.6

32.6

31.4

31.8

31.9

32.8

31.5

31.6

32.2

32