Take away 32 from the product of 6 and a number

A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estima

liq [111]

Answer:

a) $\bar X=9.07$

b) The 95% confidence interval is given by (8.197;9.943)

c) $m=2.14 \frac{1.580}{\sqrt{15}}=0.873$

d) 3 possible ways

1) Increasing the sample size n.

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

Step-by-step explanation:

Notation and definitions

n=15 represent the sample size

$\bar X= 9.07$ represent the sample mean

$s=1.580$ represent the sample standard deviation

m represent the margin of error

Confidence =95% or 0.95

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".

Part a: Find the point estimate of the population mean.

The point of estimate for the population mean $\mu$ is given by:

$\bar X =\frac{\sum_{i=1}^{n} x_i}{n}$

The mean obteained after add all the data and divide by 15 is $\bar X=9.07$

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by:

$df=n-1=15-1=14$

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,14)" for $t_{\alpha/2}=-2.14$

"=T.INV(1-0.025,14)" for $t_{1-\alpha/2}=2.14$

The critical value $tc=\pm 2.14$

Part c: Calculate the margin of error (m)

First we need to calculate the standard deviation given by this formula:

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$

s=1.580

The margin of error for the sample mean is given by this formula:

$m=t_c \frac{s}{\sqrt{n}}$

$m=2.14 \frac{1.580}{\sqrt{15}}=0.873$

Part b: Calculate the confidence interval

The interval for the mean is given by this formula:

$\bar X \pm t_{c} \frac{s}{\sqrt{n}}$

And calculating the limits we got:

$9.07 - 2.14 \frac{1.580}{\sqrt{15}}=8.197$

$9.07 + 2.14 \frac{1.580}{\sqrt{15}}=9.943$

The 95% confidence interval is given by (8.197;9.943)

Part d: How can we reduce the margin of error?

We can reduce the margin of error on the following ways:

1) Increasing the sample size n.

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

3 0

3 years ago

If you know the diameter of a circle, which statement describes how to find the area?

Rudik [331]

Well to find the area of a circle Pie times r^2. But If you already have the diameter, you could either split the diameter in half, and do the regulaur formula, OR you could ude this formula ----> Pie times The diameter

7 0

2 years ago

Read 2 more answers

Y=2x-5 -3x - 4y=-2

Whitepunk [10]

Answer:

y=-x/5 =3/5. that is how it is.

8 0

2 years ago

A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed below: 67.4

skad [1K]

Answer:

a) $\bar X =\frac{67.401+67.400+67.402+67.396+67.406+67.401+67.396+67.401+67.405+67.404}{10}=67.401$

b) The sample deviation is calculated from the following formula:

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And for this case after replace the values and with the sample mean already calculated we got:

$s=0.0036$

If we assume that the data represent a population then the standard deviation would be given by:

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}$

And then the deviation would be:

$\sigma =0.00319$

Step-by-step explanation:

For this case we have the following dataset:

67.401, 67.400, 67.402, 67.396, 67.406, 67.401, 67.396, 67.401, 67.405, and 67.404

Part a: Determine the most probable value.

For this case the most probably value would be the sample mean given by this formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

And if we replace we got:

$\bar X =\frac{67.401+67.400+67.402+67.396+67.406+67.401+67.396+67.401+67.405+67.404}{10}=67.401$

Part b: Determine the standard deviation

The sample deviation is calculated from the following formula:

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And for this case after replace the values and with the sample mean already calculated we got:

$s=0.0036$

If we assume that the data represent a population then the standard deviation would be given by:

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}$

And then the deviation would be:

$\sigma =0.00319$

3 0

3 years ago

Need help with this question , pls help

notka56 [123]

Answer:

A = 80g B = 200g

Step-by-step explanation for A:

First, you would find what the serving size is divided by to get the number of people needed to feed 6/3 = 2. Then take that number (3) and divided it by the fish (240g) to get 240/3 = 80.

Step-by-step explanation for B:

You will first need to find how much butter goes into ONE pie by dividing 80 by 6 which is 1.33333333333333. Then do 1.333333333333333 times the number of people to feed (15) to get 200.

8 0

1 year ago