Question

State your conclusion to the following hypothesis test.

Answer 1

Answer:

Part A

a. There is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05

Part B

$\hat Y$ = 17.9·(x) + 1.6

Part C

The teen pregnancy rate in Florida is 6.54

Step-by-step explanation:

The percentage of graduates that find full-time employment in their fields within the first year of graduation = 87%

The significant level of the hypothesis test = 5% = 0.05

The p-value = 0.07

Given that the testing conditions are met, we have;

The p-value is larger than the significant level of 0.05, therefore, it cannot be concluded that there is significant difference between the two rates

Therefore;

There is not enough statistical evidence available to come to a conclusion that the placement rate of full-time students has reduced below the given 87% because from the statistics, the p-value is larger than 0.05.

Part B

Number of Pages, x; 7, 12, 4, 14, 25, 30

Cost, y; 128, 213, 75, 250, 446, 540

The regression analysis formula is;

Y = a + b·X

We have;

$b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}$

∴ b = (6×34602-92×1652)/(6×1930 - 92²) ≈ 17.852

$a = \dfrac{\sum Y - b\sum X}{N}$

a = (1652 - 17.852 × 92)/6 ≈ 1.6

∴ Y ≈ 17.9·(x) + 1.6

Part C

The given regression model is y = 4.3 + 1.4(x)

Therefore, at x = 1.6, we get;

y = 4.3 + 1.4 × 1.6 = 6.54

The suggests that the teen pregnancy rate in Florida is 6.54.