The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498.a. To perform this study, we should form a null hypothesis stating that the average is 100,000. (Please fill in only one of the following: "less than", "less than or equal to", "equal to", "greater than", "greater than or equal to". Please do not use symbols.)b. At the 10% significant level, the p-value/statistics is (Please keep three decimal points) so we should the null hypothesis (Please only fill in "reject" or "not reject".).c. Hence, we may conclude that the average increased (Please only fill in "has" or "has not") and the probability that our conclusion is correct is at least percent.

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ equal to 100000

For the alternative hypothesis,

H1: µ greater than 100000

This is a right tailed test

Since the population standard deviation is nit given, the distribution is a student's t.

Since n = 200

Degrees of freedom, df = n - 1 = 200 - 1 = 199

t = (x - µ)/(s/√n)

Where

x = sample mean = 103157

µ = population mean = 100000

s = samples standard deviation = 27498

t = (103157 - 100000)/(27498/√200) = 1.62

We would determine the p value using the t test calculator.

p = 0.053

Alpha = 10% = 0.1

Since alpha, 0.1 > than the p value, 0.053, then

b) At the 10% significant level, the p-value/statistics is 0.053, so we should not reject the null hypothesis.

c) Hence, we may conclude that the average has not increased and the probability that our conclusion is correct is at least 90 percent.

2425

step-by-step explanation:

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w