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g In a certain rural county, a public health researcher spoke with 111 residents 65-years or older, and 28 of them had obtained

Marat540 [252]

Answer:

95% confidence interval for the percent of the 65-plus population that were getting the flu shot is [0.169 , 0.331].

Step-by-step explanation:

We are given that in a certain rural county, a public health researcher spoke with 111 residents 65-years or older, and 28 of them had obtained a flu shot.

Firstly, the Pivotal quantity for 95% 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 residents 65-years or older who had obtained a flu shot = $\frac{28}{111}$ = 0.25

n = sample of residents 65-years or older = 111

p = population proportion of residents who were getting the flu shot

Here for constructing 95% confidence interval we have used One-sample z test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.25-1.96 \times {\sqrt{\frac{0.25(1-0.25)}{111} } }$ , $0.25+1.96 \times {\sqrt{\frac{0.25(1-0.25)}{111} } }$ ]

= [0.169 , 0.331]

Therefore, 95% confidence interval for the percent of the 65-plus population that were getting the flu shot is [0.169 , 0.331].

7 0

2 years ago

Use z scores to compare the given values.

Effectus [21]

Answer:

The answer is given below

Step-by-step explanation:

Z score is used to measure by how many standard deviations the raw score is above or below the mean. It is given by the formula:

$z=\frac{x-\mu}{\sigma}\\ \\Where\ \mu=mean, x=raw\ score, \sigma=standard\ deviation$

For the male:

μ = 3259.8 g, σ = 869.7 g

Hence for a male who weighs 1600 g, the z score is:

$z=\frac{x-\mu}{\sigma} =\frac{1600-3259.8}{869.7}=-1.91$

For the female:

μ = 3000.9 g, σ = 550.8 g

Hence for a female who weighs 1600 g, the z score is:

$z=\frac{x-\mu}{\sigma} =\frac{1600-3000.9}{550.8}=-2.54$

Since the z score for the male is z= -1.91 and the z score for the female is z= -2.54 the male has the weight that is more extreme.

6 0

2 years ago

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't

N76 [4]

Answer:

I believe its $5492.99

Step-by-step explanation:

First I divided $160 by 3%.

Than I multiplied my answer by 1.03.

4 0

3 years ago

Read 2 more answers

Plz help me help me help me

exis [7]

The answer is this :) hope I helped

7 0

2 years ago

Read 2 more answers

If a solid has faces that consist of 2 equilateral triangles and 3 congruent rectangles, what type of solid is it?

Burka [1]

A right triangular prism is a solid that has faces that consist of 2 equilateral triangles and 3 congruent rectangles. It is also described to have two parallel faces, and 3 other faces that belong to the same place (and are not parallel to the parallel pair of faces).

7 0

3 years ago