5. the superintendent of the local school district claims that the children in her district are brighter, on average, than the general population. to determine the aptitude of her district's children, a study was conducted. the results of her district's test scores were: 105, 109, 115, 112, 124, 115, 103, 110, 125, 99. if the mean of the general population of school children is 106, what could be said about her claim? use alpha = .05

We conclude that children in district are brighter, on average, than the general population.

Step-by-step explanation:

We are given the following data set:

105, 109, 115, 112, 124, 115, 103, 110, 125, 99

Formula:

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 642.1

We are given the following in the question:  

Population mean, μ = 106

Sample mean, = 111.7

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 8.44

First, we design the null and the alternate hypothesis

We use one-tailed(right) t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                  

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

We conclude that children in district are brighter, on average, than the general population.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

step-by-step explanation: