Mathematics, 20.03.2020 03:09, arielpraczko1

A large employer would like to estimate the proportion of employees who are dissatisfied with their jobs. They take a random sample of 60 employees and survey them on their current feelings toward their job. Twenty-four of the employees surveyed stated they were moderately to very dissatisfied with their current position. Calculate a 99% confidence interval that estimates the true proportion p, of all employees who are dissatisfied. Group of answer choices 99%CI(0.261, 0.539) 99%CI(0.296, 0.504) 99%CI(0.237, 0.563) 99%CI(0.276, 0.524)

Answers: 1

Show answers

Answers

answered: angelica7773

99%CI (0.237, 0.563)

Step-by-step explanation:

The z-score for a 99% confidence interval is Z = 2.576

The proportion of workers in the sample who are dissatisfied with their position is given by the number of people who answered that "they were dissatisfied", divided by the total sample of n = 60 employees.

$p=\frac{24}{60}=0.4$

The confidence interval for a proportion 'p' is:

$p\pm Z*\sqrt{\frac{p*(1-p)}{n}}\\p\pm 2.576*\sqrt{\frac{0.4*(1-0.4)}{60}} \\L=0.4-0.163=0.237\\U=0.4+0.163=0.563$

The 99% confidence interval is CI (0.237, 0.563).

answered: Alysssssssssssa

99% confidence interval that estimates the true proportion p, of all employees who are dissatisfied is [0.237 , 0.563].

Step-by-step explanation:

We are given that a large employer would like to estimate the proportion of employees who are dissatisfied with their jobs. They take a random sample of 60 employees and survey them on their current feelings toward their job. Twenty-four of the employees surveyed stated they were moderately to very dissatisfied with their current position.

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

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

where, $\hat p$ = proportion of employees who stated that they were moderately to very dissatisfied with their current position in a sample of 60 = $\frac{24}{60}$ = 0.40

n = sample of employees = 60

p = true proportion

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

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

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

significance level 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 =[ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.40-2.5758 \times {\sqrt{\frac{0.40(1-0.40)}{60} } }$ , $0.40+2.5758 \times {\sqrt{\frac{0.40(1-0.40)}{60} } }$ ]

= [0.237 , 0.563]

Therefore, 99% confidence interval that estimates the true proportion p, of all employees who are dissatisfied is [0.237 , 0.563].

answered: Guest

Where is the picture

answered: Guest

It's all about the 4

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 17:30, marie1211

The table shows the balance of a money market account over time. write a function that represents the balance y(in dollars) after t years.

Answers: 2

continue

Mathematics, 21.06.2019 18:00, vianney84

1. a parachutist is 800 feet above the ground when she opens her parachute. she then falls at a constant rate of 5 feet per second. select the equation that represents this situation. h = -800t + 5 y = -5x + 800 h = 5t - 800 y = 800x + 5 i need

Answers: 1

continue

Mathematics, 21.06.2019 18:30, christinaS7696

First to answer all gets a donation question 3(multiple choice worth 1 points) (04.01 lc) which of the following levels is lower than cells in the hierarchy of organization of living things? molecules organs organ systems tissues question 4(multiple choice worth 1 points) (04.01 lc) which of these represents an individual form of life such as an animal, plant, or single-celled life form? organ organism organ system tissue question 5(multiple choice worth 1 points) (04.03 lc) what are the green structures inside plant cells where photosynthesis takes place called? chloroplast mitochondrion nucleus vacuole question 6(multiple choice worth 1 points) (04.03 lc) which of the following best matches a part of a living cell with the function it performs? cytoplasm: fluid which carries the nucleus and other organelles vacuole: fluid which carries the nucleus and other organelles cytoplasm: directs all of the cell's activities vacuole: directs all of the cell's activities question 7(multiple choice worth 1 points) (04.03 mc) read the table below. organelles of plant cells present in both plants and animals present in plants but not animals small in animals but large in plants organelle a organelle b organelle c which statement is most likely correct? organelle a is chloroplast, organelle b is cytoplasm, and organelle c is nucleus. organelle a is mitochondrion, organelle b is cytoplasm, and organelle c is nucleus. organelle a is cell wall, organelle b is chloroplast, and organelle c is mitochondrion. organelle a is mitochondrion, organelle b is chloroplast, and organelle c is vacuole. question 8(multiple choice worth 1 points) (04.03 mc) what will most likely happen in the absence of a nucleus? genetic information will not be transmitted by the cell. energy will not be released during cellular respiration. the cell will not store food, water, nutrients, and waste. the cell will lose its shape and structure.

Answers: 1

continue

Mathematics, 21.06.2019 20:00, Abdirisack3250

How to find the exponential function y=ca^x, with points (1,2) and (2,1)

Answers: 2

continue

Do you know the correct answer?

A large employer would like to estimate the proportion of employees who are dissatisfied with their...