The lowest temperature on May 15 is 23 as warm as the warmest temperature on May 15. The lowest temperature on May 15 is 60ºF.

In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

Step-by-step explanation:

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

3 years ago

An architect draws a blueprint of a house. He draws the living room on the blueprint as 4.5 in. long by 6 in. wide with a scale

s2008m [1.1K]

Answer:

the answer is 8.5

Step-by-step explanation:

yeet

8 0

3 years ago

Read 2 more answers

Elena surveyed her classmates to see how many like to make jewelry. When she asked 20 of her classmates, 50 percent said they li

nordsb [41]

10 students of Elena's classmates like to make jewellery.

<u>Step-by-step explanation:</u>

Let total no.of classmates who liked the jewellery = x

Here, in the given problem, given she asked her classmates '20'. So, it clearly shows that total number of students/classmates = 20. Also, in that, 50% said like to make jewellery. Now find 'x' as below,

$x = 50 \% \text { of } 20$

$x = \frac{50}{100} \times 20$

$x = 10$

Hence, the total number of classmates who liked to make Jewellery = 10

5 0

3 years ago

An adjustable ladder on the back of the firetruck is needed for firefighters to climb to very high buildings. The maximum angle

torisob [31]

Cos 70 = horizontal distance /
100 horizontal distance = 100 cos 70 = 32.2feet

3 0

3 years ago

Amanda placed her finger on the origin of a regular coordinate plane. She marked a point after moving her finger 1 unit to the l

Lubov Fominskaja [6]

Answer:

( x , y ) = ( -1 , - 5 )

Step-by-step explanation:

Solution:-

- The rectangular coordinate system ( Cartesian ) is defined by two independent variables namely, "x and y".

- The values of both varibales lie on the horizontal and vertical line respectively, ( x & y ).

- The values on the horizontal axis also known as the x-axis is marked with a referece of x = 0 ( origin ). All the values to the right of the point of origin are denoted as positive units and all values to the left of the point of origin are denoted as negative units.

- Similarly, The values on the vertical axis also known as the y-axis is marked with a referece of y = 0 ( origin ). All the values to the above the point of origin are denoted as positive units and all values below of the point of origin are denoted as negative units.

- The axis are conventionally oriented such that 90 degrees angle is formed in between them and always denoted in the counter-clockwise direction.

In other words, if +x is pointing to the right then the +y will be pointed in the direction when +x is rotated counter clockwise to 90 degrees; hence, points upward.

- When Amanda starts off at the origin she is at the order pair ( 0 , 0 ).

- She then moves her finger 1 unit to left ( -x ) and 5 units down ( -y ). Hence, she moves 1 unit along the -x direction and then moves 5 units down along -y direction.

Hence, she is at an ordered pair ( x , y ) = ( -1 , - 5 ) .

3 0

3 years ago