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Aleks [24]
3 years ago
9

An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sa

mple size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that Ơ = 19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
(a)The required sample size is ____. (Round up to one integer as needed)
(b)Is this sample size reasonable?
Mathematics
2 answers:
sleet_krkn [62]3 years ago
8 0
We use the formula:
x± s <span>t_<span>(1−c)/2 / </span></span>√n = 5

(1 - c)/2 = (1 - 0.95) / 2 = 0.025
Using the t score calculator at this value, at the 95% confidence internval,
t = 0.5080, So
100 - 19(0.5080) / √n = 5
Solving for n
n = 97

a) 97
b) yes
yuradex [85]3 years ago
7 0
Hello there.
<span>An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that Ơ = 19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. 
(a)The required sample size is ____. (Round up to one integer as needed)
(b)Is this sample size reasonable?
</span>
A) 97
B) True/Yes
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At what interest rate must you invest $4500 to have $7,000 after 6 years, if the interest is compounded quarterly?
labwork [276]

Answer:

The amount is $8358.7 and the interest is $3858.7.

Step-by-step explanation:

Explanation

STEP 1: To find amount we use formula:

A=P(1+rn)n⋅t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

P=$4500 , r=7% , n=2 and t=9 years

After plugging the given information we have

AAAA=4500(1+0.072)2⋅9=4500⋅1.03518=4500⋅1.857489=8358.7

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4 0
3 years ago
19x+rx= -37x+w what is the x
seraphim [82]

Answer:

x = w / (56 + r)

Step-by-step explanation:

Given the equation :

19x + rx= -37x + w ; find x

Collecting like terms

19x + rx + 37x = w

Factorizing x in the Left hand side

x(19 + 37 + r) = w

x(56 + r) = w

Therefore we can obtain x by dividing both sides by (56 + r)

x(56 + r) / (56 + r) = w / (56 + r)

x = w / (56 + r)

5 0
3 years ago
Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothes
PolarNik [594]

Answer:

Option A) 2.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 46

Sample mean, \bar{x} = 50

Sample size, n = 25

Alpha, α = 0.05

Population standard deviation, σ = 8

First, we design the null and the alternate hypothesis

H_{0}: \mu \leq 46\\H_A: \mu > 46

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{50 - 46}{\frac{8}{\sqrt{25}} } =2.5

Option A) 2.5

6 0
3 years ago
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