The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A random sample of 16 residents of Wilmington, Delaware, had a mean of $52,500 with a standard deviation of $9,500.
At the 0.050 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?

At 5% level of significance there is enough evidence to concluded that the residents of Wilmington, Delaware, have more income than the national average.

Step-by-step explanation:

The national average income of United states is, $44,500.

The hypothesis to test whether the residents of Wilmington, Delaware, have more income than the national average, can be defined as:

H₀: The residents of Wilmington, Delaware, does not have more income than the national average, i.e. μ < $44,500.

Hₐ: The residents of Wilmington, Delaware, have more income than the national average, i.e. μ > $44,500.

It is provided that the distribution of incomes follows a normal distribution.

Given:

The significance level of the test is, α = 0.05.

As the sample size is small and the population standard deviation is not provided, use the t-test for single mean.

The test statistic is:

Decision Rule:

If the p value of the test is less than the significance level then the null hypothesis is rejected.

Compute the p value as follows:

Use the t-table for probability.

The p-value = 0.002 < α = 0.05.

The null hypothesis will be rejected at 5% significance level.

Conclusion:

As the null hypothesis is rejected it implies that the residents of Wilmington, Delaware, have more income than the national average.

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet