What equation represents the graph below?

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The es

Mrrafil [7]

Answer:

The minimum sample size required to construct a 95% confidence interval for the population mean is 65.

Step-by-step explanation:

We are given the following in the question:

Population standard deviation,

$\sigma = 3.10\text{ milligrams}$

We need to construct a 95% confidence interval such that the estimate is within 0.75 milligrams of the population mean.

Thus, the margin of error must me 0.75

Formula for margin of error:

$z_{critical}\times \dfrac{\sigma}{\sqrt{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$0.75 = 1.86\times \dfrac{3.10}{\sqrt{n}}\\\\\sqrt{n} = \dfrac{1.96\times 3.10}{0.75}\\\\\sqrt{n} = 8.101\\\Rightarrow n = 65.63\approx 65$

Thus, the minimum sample size required to construct a 95% confidence interval for the population mean is 65.

5 0

3 years ago

A recent survey showed that in a sample of 100 elementary school teachers, 15 were single. In a sample of 180 high school teache

trapecia [35]

Answer:

By using hypothesis test at α = 0.01, we cannot conclude that the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single

Step-by-step explanation:

let p1 be the proportion of elementary teachers who were single

let p2 be the proportion of high school teachers who were single

Then, the null and alternative hypotheses are:

$H_{0}$ : p2=p1

$H_{a}$ : p2>p1

We need to calculate the test statistic of the sample proportion for elementary teachers who were single.

It can be calculated as follows:

$\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }$ where

p(s) is the sample proportion of high school teachers who were single ( $\frac{36}{180} =0.2$ )
p is the proportion of elementary teachers who were single ( $\frac{15}{100} =0.15$ )