It costs £8 to go on a bowling trip.

In a survey of US adults, twenty percent say they never exercise. This is the highest level seen in five years.

Andrews [41]

Answer:

$0.20 - 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.175$

$0.20 + 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.225$

The 95% confidence interval would be given by (0.175;0.225)

Step-by-step explanation:

Assuming this question: In a survey of 1000 US adults, twenty percent say they never exercise. This is the highest level seen in five years.1 Find a 95% confidence interval for the proportion of US adults who say they never exercise. Round your answers to three decimal places.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.20 - 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.175$

$0.20 + 1.96\sqrt{\frac{0.2(1-0.2)}{1000}}=0.225$

The 95% confidence interval would be given by (0.175;0.225)

6 0

3 years ago

PLEASE HELP PICTURE SHOWN

den301095 [7]

Option C and D is correct .....

4 0

3 years ago

rita put $2,000 in a bank account that pays at 4% annual simple interest at the end of 9 months he decides to take her money out

Illusion [34]

Answer:

$666.66

Step-by-step explanation:

4%/12=0.33333

0.33333*9= 3%

2,000/3=$666.66

2,000+666.66=$2,666.66

6 0

3 years ago

Determine whether the relation is a function: {(6, 1), (8, –3), (6, 7)}.

ICE Princess25 [194]

Hello there! The answer would be the first one, or No. At least one output results in two inputs.

When dealing with functions: you must remember that x does not repeat. So, lets look at the relation given, {(6, 1), (8, –3), (6, 7)}. You can see that x does repeat, so this is not a function. This eliminates second and fourth option choices. Out of the options A and C, A would be your choice since x is the input value and y is the output value, and there are two input values.

Hope his helps and have a great day!

5 0

4 years ago

Pls help: without graphing determine whether the function represents exponential growth or exponential decay. Then find y-interc

Mrac [35]

Given

$0.99(\frac{1}{3})^x$

To determine whether the function represents exponential growth or exponential decay, and the y-intercept.

now,

It is given that,

$0.99(\frac{1}{3})^x$

The exponential functions are of the form,

$y=ab^x$

If a is positive and b is greater than 1, then it represents exponential growth.

And, if a is positive and b is greater than 0 and less than 1, then it represents exponential decay.

Since b=1/3<1.

Then, the given function represents exponential decay.

The y- intercept of the function is,

$\begin{gathered} y=0.99(\frac{1}{3})^x \\ \text{When x=0.} \\ y=0.99(\frac{1}{3})^0 \\ y=0.99 \end{gathered}$

Hence, the y-intercept is 0.99.

6 0

1 year ago