A serving of crackers has 1.5 grams of fat.

A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week

Levart [38]

Answer:

99% confidence interval for the population proportion of employed individuals is [0.104 , 0.224].

Step-by-step explanation:

We are given that a simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week.

Of the 250 employed individuals surveyed, 41 responded that they did work at home at least once per week.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of individuals who work at home at least once per week = $\frac{41}{250}$ = 0.164

n = sample of individuals surveyed = 250

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

99% confidence interval for p = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.164-2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ , $0.164+2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ ]

= [0.104 , 0.224]

Therefore, 99% confidence interval for the population proportion of employed individuals who work at home at least once per week is [0.104 , 0.224].

7 0

3 years ago

Find the slope of everyline that is perpendicular to the graph of the equation y-2/3x=2

Flauer [41]

Answer:

m= -3/2

Step-by-step explanation:

First, we must find the slope of the line given. We are given the equation:

y-2/3x=2

We must get this equation in slope-intercept form: y=mx+b (where m is the slope and b is the y-intercept). In order to do this, we must get y isolated.

2/3x is being subtracted from y. We want to preform the inverse, so we should add 2/3x to both sides.

y-2/3x+2/3x=2+2/3x

y=2+2/3x

Rearrange the terms.

y= 2/3x+2

Now the equation is in slope intercept form. (y=mx+b). 2/3 and x are being multiplied, so we know that the slope is 2/3.

Now, we have to find the perpendicular slope. Perpendicular lines have negative reciprocal slopes.

1. Negative

m=2/3

Negate the slope.

m= -2/3

2. Reciprocal

m= -2/3

Flip the numerator (top number) and denominator (bottom number).

m= -3/2

The perpendicular slope is -3/2

3 0

3 years ago

Find the geometric mean between 4 and 1/4. Show your work.

Darya [45]

Answer:

2.125

Step-by-step explanation:

3 0

3 years ago

PLEASE HELP ME *algebra 2*

Blizzard [7]

I hope this helpss.

8 0

3 years ago

Plz help me on this question

zhuklara [117]

I cant see it please send another pic of it. closer to the screen.

5 0

4 years ago