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rosijanka [135]
3 years ago
14

A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standa

rd deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 4% of 70%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
Mathematics
1 answer:
swat323 years ago
4 0
All our answers lie in the above statement.

Confidence Level:
The creator claims that 9 out 10 students will have the average score in the said range. Or in other words we can say that the creator is 90% confident about the result of the field test. So the confidence level is 90%. 

Margin of Error:
The average score lies within 4% of 70%. This means the margin of error is 4% i.e. the average scores can deviate from 70% by 4% .

Confidence Interval:
Lower Limit = 70% - 4% = 66%
Upper Limit = 70% + 4% = 74%

Interpretation:
The exam creator is 90% confident that the average scores of seniors will be between 66% and 74%. 
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A sample of 38 observations is selected from one population with a population standard deviation of 3.4. The sample mean is 100.
kaheart [24]

Answer:

a. two-tailed test

b. reject H0 if Z>1.96 or Z<-1.96

c. Z = 1.73

d. we have failed to reject the null hypothesis

e. P-value = 0.0418

Step-by-step explanation:

We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.

We need to find our critical value:

Zα/2 = Z(0.05/2) = 0.025

If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96

The Z test will be done using the next equation:

Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2

Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:

Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73

Z<1.96, therefore we have failed to reject the null hypothesis

The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis

4 0
3 years ago
Jason wants to plant 66 carrot seeds and 44 onion bulbs. He would like to plant them so
dexar [7]

The greatest number of plants he can have in each row is 22

He would have 3 rows of carrots

He would have 2 rows of onions

<h3>Greatest Common Factor</h3>

From the question, we are to determine the greatest number of plants he can have in each row

From the given information,

Jason wants to plant 66 carrot seeds and 44 onion bulbs

The greatest number of plants he can have in each row is the greatest common factor of 66 and 44

Factors of 66: 1, 2, 3, 6, 11, 22, 33, and 66

Factors of 44:  1, 2, 4, 11, 22 and 44

The greatest common factor of 66 and 44 is 22

Thus,

The greatest number of plants he can have in each row is 22

He would have 66/22 rows of carrots

66/22 = 3

Thus,

He would have 3 rows of carrots

He would have 44/22 rows of onions

44/22 = 2

Hence, he would have 2 rows of onions

Learn more on Greatest Common Factors here: brainly.com/question/5535901

#SPJ1

3 0
2 years ago
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
Elanso [62]

Answer:

The sum is a binomial with a degree of 6

Step-by-step explanation:

we have

(3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)

Group terms that contain the same variable

(3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y

0-2xy^{5}+3x^{4}y

-2xy^{5}+3x^{4}y

The sum is a binomial ( two terms) with a degree of 6  

-2xy^{5} has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)

6 0
3 years ago
Read 2 more answers
What angle in degrees has a sine of approximately 0.5736???
statuscvo [17]

Answer:

35º

Step-by-step explanation:

90-55 = 35º

6 0
3 years ago
Read 2 more answers
Explain how to graph the following including asymptotes and key features. f(x)=3^x+2
sattari [20]

Answer:

y=2

Step-by-step explanation:

7 0
3 years ago
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