HELP! 10 POINTS AND BRAINLIEST

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

a

$336.04 < \mu < 443.96$

b

The margin of error will increase

c

The margin of error will decreases

d

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

So

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

$n \ \ \alpha \ \ \frac{1}{E^2 }$

So if the sample size increases the margin of error decrease

The sample proportion is mathematically represented as

$\r p = \frac{210}{500}$

$\r p = 0.42$

Given that the confidence level is 0.99 the level of significance is $\alpha = 0.01$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }$

=> $E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }$

=> $E = 0.0093$

The 99% confidence interval is

$\r p - E < p < \r p + E$

$0.42 - 0.0093 < p < 0.42 + 0.0093$

$0.4107 < p < 0.4293$

4 0

4 years ago

Which of the following statements best describes the graph of x + y = 4?

joja [24]

Answer: The correct option is, It is a line joining the points whose x and y coordinates add up to 4.

Step-by-step explanation:

The given equation is, $x+y=4$

when we take x = 1 then

$1+y=4$

$y=3$

when we take x = 2 then

$2+y=4$

$y=2$

From this we conclude that the sum of 'x' and 'y' coordinates is always equal to 4.

Hence, the correct answer is, It is a line joining the points whose x and y coordinates add up to 4.

5 0

3 years ago

What are the point for a 90 degree rotation counterclockwise about the origin

Korvikt [17]

Answer:

Here is your solution.

6 0

3 years ago

For what values of y:s the value of the fraction 4.5−2y/5 less than the value of the fraction 2−3y/10 ?

Andre45 [30]

Answer:

7 < y

Step-by-step explanation:

The relation you're interested in is ...

(4.5 -2y)/5 < (2 -3y)/10

9 -4y < 2 -3y . . . . . . . . . multiply by 10

7 < y . . . . . . . . . . . . . . . . add 4y-2

The value of the first fraction will be less than that of the second fraction for values of y greater than 7.

4 0

3 years ago

An occupational safety officer for a large company is conducting a study to investigate back problems in office workers who use

Oduvanchick [21]

Answer:

с. A matched pairs t-interval for a mean difference.

Step-by-step explanation:

With the sample, we will have possession of the sample mean and of the sample standard deviation, which means that the t-distribution will be used.

We want to find the mean number of back problems for each sample, and estimate the difference. Since the groups are similar, with only the positions in which they work being different, we have matched pairs. So the correct answer is given by option c.

7 0

3 years ago