Estimate the sum by rounding the numbers to the nearest hundred and then adding: 539 + 221

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 397 elementary school teache

Tju [1.3M]

Answer:

The 95% confidence interval would be given (0.0109;0.1651).

We are confident at 95% that the difference between the two proportions is between $0.0109 \leq p_{elementary} -p_{High school} \leq 0.1651$

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion for elementary school

$\hat p_A =\frac{226}{397}=0.569$ represent the estimated proportion for elementary school

$n_A=397$ is the sample size required for Brand A

$p_B$ represent the real population proportion for high school teachers

$\hat p_B =\frac{129}{268}=0.481$ represent the estimated proportion for high school teachers

$n_B=268$ is the sample size required for Brand B

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.569-0.481) - 1.96 \sqrt{\frac{0.569(1-0.569)}{397} +\frac{0.481(1-0.481)}{268}}=0.0109$

$(0.569-0.481) + 1.96 \sqrt{\frac{0.569(1-0.569)}{397} +\frac{0.481(1-0.481)}{268}}=0.1651$

And the 95% confidence interval would be given (0.0109;0.1651).

We are confident at 95% that the difference between the two proportions is between $0.0109 \leq p_{elementary} -p_{High school} \leq 0.1651$

5 0

3 years ago

What is a question that is easier to answer using a stem-and-leaf plot than a dot plot?

bagirrra123 [75]

Answer:

steam plot

Step-by-step explanation:

because the stem plot is easy to use

3 0

2 years ago

Read 2 more answers

How do i do these without a calculator

77julia77 [94]

Answer:

Step-by-step explanation:

ok just try to figure out the square root if their no certain number you can do an estimate.

For example 625 squared root is 125

For higher one you can use prime factorization to get the prime factors and with that you have to make groups of numbers with the number left side

8 0

3 years ago

Choose the set that is the possible side lengths of a right triangle.

irina1246 [14]

Answer:

D

Step-by-step explanation:

Mathematically, for us to have a right triangle, Pythagoras’ theorem must be obeyed

From the theorem, the square of the hypotenuse (longest side) equals the sum of the squares of the two other sides

Let us take a look at the given set of numbers:

2 square is not same as 1 squared + 1 squared

9 squared is not equal to 3 squares + 5 squared

7 squared is not equal to 4 squared + 3 squared

But;

root 2 squared equals 1 squared plus 1 squared and that is our answer

5 0

3 years ago

Consider the table. Explain how to use a graph to find additional equivalent ratios.<br>plz hurry

Blizzard [7]

Answer:

Plot the ordered pairs (2, 5) and (4, 10). Start at (4, 10). Move right 2 and up 5, and then plot a point. Use the same rate to plot other points. You could also draw a line through the origin and the two given points. Any point on the line represents an equivalent ratio.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers