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4 years ago

Choose the answer that best completes the sentence.

Mathematics

1 answer:

kotegsom [21]4 years ago

3 0

Name for natural numbers are integers

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5. The superintendent of the local school district claims that the children in her district are brighter, on average, than the g

anygoal [31]

Answer:

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:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1117}{10} = 111.7$

Sum of squares of differences = 642.1

$S.D = \sqrt{\frac{642.1}{49}} = 8.44$

We are given the following in the question:

Population mean, μ = 106

Sample mean, $\bar{x}$ = 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

$H_{0}: \mu = 106\\H_A: \mu > 106$

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

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{111.7 - 106}{\frac{8.44}{\sqrt{10}} } = 2.135$

Now,

$t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = 1.833$

Since,

$t_{stat} > t_{critical}$

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.

4 0

3 years ago

The value of 4 less than the product of 0.25 and x is greater than 6.

ella [17]

Answer:

0.25x - 4 > 6

7 0

3 years ago

Emma and her friend arrive in Langdale and decide to go for a coffee. The owner of the café is giving a free cupcake to every 4t

nasty-shy [4]

If the owner is giving a free cupcake to every 4th customer. Then the easiest way to do this is to follow the 4 times table: 4, 8, 12, 16, 20

So the answer is No, Emma will not be receiving a free cupcake as she is the 17th customer and doesn't fall into the 4th customer pattern.

5 0

3 years ago

Aaron can select between the following payment plans. Payment plan 1: aaron will get paid $10 the first week and each subsequent

Nataly_w [17]

Answer:

Payment plan 2

Step-by-step explanation:

8 0

4 years ago

makvit [3.9K]

Answer:

3.159 is answer for the solution

3 0

3 years ago