Someone please help me?!?!

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

malfutka [58]

Answer:

99% confidence interval for the true mean number of words a third grader can read per minute is [35.5 , 35.9].

Step-by-step explanation:

We are given that a sample of 1584 third graders, the mean words per minute read was 35.7. Assume a population standard deviation of 3.3.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean words per minute read = 35.7

$\sigma$ = population standard deviation = 3.3

n = sample of third graders = 1584

$\mu$ = population mean number of words

Here for constructing 99% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.58 & 2.58}

P(-2.58 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.58) = 0.99

P( $-2.58 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.58 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $35.7-2.58 \times {\frac{3.3}{\sqrt{1584} } }$ , $35.7+2.58 \times {\frac{3.3}{\sqrt{1584} } }$ ]

= [35.5 , 35.9]

Therefore, 99% confidence interval for the true mean number of words a third grader can read per minute is [35.5 , 35.9].

6 0

3 years ago

A cubic foot contains roughly 7 1/2 gallons. How many cubic feet are there in a tank containing 34 1/2 gallons

svlad2 [7]

Answer:

4.6 cubic feet

Step-by-step explanation:

take 34 1/2 gallons and divide it by 7 1/2 gallons

34.5 divided by 7.5 = 4.6

6 0

3 years ago

Factor completely 3x 2 + 2xy - y 2

sergij07 [2.7K]

Answer:

Final answer is $(3x-y)(x+y)$ .

Step-by-step explanation:

Given expression is $3x^2+2xy-y^2$ .

Now we need to factor the given expression $3x^2+2xy-y^2$ completely. Let's use factor by grouping method.

$3x^2+2xy-y^2$

$=3x^2+3xy-xy-y^2$

$=3x(x+y)-y(x+y)$

$=(3x-y)(x+y)$

Hence final answer is $(3x-y)(x+y)$ .

5 0

3 years ago

Read 2 more answers

Evaluate the expression 1/2x - 2/3y when x = 4 and y = -3

ollegr [7]

Answer:

-1

Step-by-step explanation:

Equation: 1/2x-2/3y

Swap out the x and y with the numbers.

1/2 x 4/1 -2/3 x -3

Solve.

2-3

-1

3 0

3 years ago

Read 2 more answers

According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most

AlekseyPX

Answer:

His 95% confidence interval is (0.065, 0.155).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 186, \pi = 0.11$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.11 - 1.96\sqrt{\frac{0.11*0.89}{186}} = 0.065$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.11 + 1.96\sqrt{\frac{0.11*0.89}{186}} = 0.155$

His 95% confidence interval is (0.065, 0.155).

4 0

3 years ago