Which of the following is an EXPLICIT formula for the sequence 12, 15, 18, 2 points

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

3 years ago

Is the number -14 irrational ?

Alenkinab [10]

I think it is irrational

5 0

3 years ago

Read 2 more answers

Mark the number line to show 1/4. Label 0 and 1 on the number line

emmainna [20.7K]

0 -1/8 -1/4 -1/2 -1

5 0

3 years ago

Find the next term in the sequence 15 , 34 , 55 , 78 , 103

omeli [17]

The next term in the sequence will be increased by 27. The difference between 15 and 34 is 19 The difference between 34 and 55 is 21 The difference between 55 and 78 is 23 The difference between 78 and 103 is 25 Following this pattern, the next number will be 130

6 0

3 years ago

-4/5 to the power of 2 times -3/50

Crazy boy [7]

=(-4/5)^2 * -3/50
square -4/5 first; remember -4/5^2 is the same as -4/5 * -4/5

=(-4/5 * -4/5) * -3/50
multiply -4 numerators; multiply 5 denominators

=(-4 * -4)/(5 * 5) * -3/50

=16/25 * -3/50
multiply numerators 16 & -3; multiply denominators 25 & 50

=(16 * -3)/(25 * 50)
= -48/1250

simplify by 2
= -24/625 (or -0.0384)

ANSWER: -24/625 (or -0.0384)

Hope this helps! :)

6 0

3 years ago

Read 2 more answers