Answer: A. (4, 4) and (4, 5)
Step-by-step explanation:
The same x value maps onto more than one y value.
Answer:
The test is not significant at 5% level of significance, hence we conclude that there's no variation among the discussion sections.
Step-by-step explanation:
Assumptions:
1. The sampling from the different discussion sections was independent and random.
2. The populations are normal with means and constant variance
There's no variation among the discussion sections
There's variation among the discussion sections
Df Sum Sq Mean sq F value Pr(>F)
Section 7 525.01 75 1.87 0.99986
Residuals 189 7584.11 40.13
Test Statistic = 
Since our p-value is greater than our level of significance (0.05), we do not reject the null hypothesis and conclude that there's no significant variation among the eight discussion sections.
Answer:
The two numbers are -419 and -2095.
Step-by-step explanation:
5x=y
x-y=1676
----------------
x-5x=1676
-4x=1676
x=1676/-4
x=-419
5(-419)=y
y=-2095
The mean to your problem is 87.5
Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
