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mixer [17]
3 years ago
5

orange jelly beans is 82 and that exam scores have an approximately symmetric distribution. She gives orange jelly beans to 25 r

andomly selected students and finds that these students had a sample mean score of 87 with a sample standard deviation of 10. She wants to have 95% confidence in her result. 27. Conduct a hypothesis test using the confidence interval approach. Write your answer on paper and upload a photo or scan, or else put your answer in an electronic file and upload the file. In order to earn full credit your answer must include all of the following: A statement of the confidence interval in a complete sentence using the appropriate statistical symbol. Include two decimal points in your numbers. The statistical criterion you use to determine whether to reject or fail to reject the hypothesis. The result of your test in statistical terms
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 82

For the alternative hypothesis,

µ ≠ 82

This is a 2 tailed test

Since the sample mean and sample standard deviation is given, the t test would be used to determine the test statistic. The formula is

t = (x - µ)/(s/√n)

Where

x = sample mean = 87

µ = population mean = 82

s = samples standard deviation = 10

n = 25

t = (87 - 82)/(10/√25) = 2.5

α = 1 - Confidence level

α = 1 - 0.95 = 0.05

Since α = 0.05, the critical value is determined from the t distribution table.

For the left, α/2 = 0.05/2 = 0.025

For the right of 0.025 = 1 - 0.025 = 0.975

To determine the t score from the t distribution table, we would find the degree of freedom, df and look for the corresponding α value.

df = n - 1 = 25 - 1 = 24

t score = critical value = ±2.064

In order to reject the null hypothesis, the test statistic must be smaller than - 2.5 or greater than 2.5

Since - 2.064 > - 2.5 and 2.064 < 2.5, we would fail to reject the null hypothesis.

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

Margin of error = z × s/√n

Where

s = sample standard deviation

z = t score

Margin of error = 2.064 × 10/√25

= 4.13

Confidence interval = 87 ± 4.13

the lower limit of this confidence interval is

87 - 4.13 = 82.87

the upper limit of this confidence interval is

87 + 4.13 = 91.13

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Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t
NeTakaya

Answer:

\mu = 11

\sigma = 2.08

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when Z = -1.44, X = 8. So

Z = \frac{X - \mu}{\sigma}

-1.44 = \frac{8 - \mu}{\sigma}

8 - \mu = -1.44\sigma

\mu = 8 + 1.44\sigma

Also, when X = 14, Z has a pvalue of 0.925, so when X = 8, Z = 1.44

Z = \frac{X - \mu}{\sigma}

1.44 = \frac{14 - \mu}{\sigma}

14 - \mu = 1.44\sigma

1.44\sigma = 14 - \mu

Replacing in the first equation

\mu = 8 + 1.44\sigma

\mu = 8 + 14 - \mu

2\mu = 22

\mu = \frac{22}{2}

\mu = 11

Standard deviation:

1.44\sigma = 14 - \mu

1.44\sigma = 14 - 11

\sigma = \frac{3}{1.44}

\sigma = 2.08

7 0
2 years ago
URGENT!! Need help can someone explain please!!!
forsale [732]

Answer:

The answer to your question is 1 = 69°

Step-by-step explanation:

To solve this problem remember that the sum of the internal angles in a triangle equals 180°.

Let the third angle of the triangle be x.

             39° + 30° + x = 180

Solve for x

             x = 180 - 39 - 30

             x = 111°

Angle x and angle 1 are supplementary so their sum equals 180°.

            111° + 1 = 180

                      1 = 180 - 111

                       1 = 69°      

5 0
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Answer:

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Step-by-step explanation:

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6 0
3 years ago
For which function does f (-8) = f (8) ?
nignag [31]

Answer:

Step-by-step explanation:

Can you give me more information on the question, so i can make sure that i give you the correct answer . I think its A but not totally for sure

8 0
3 years ago
Y=(3/5)x -3 and 5y =3x-10 these lines are and the second question?
azamat
Look at the first line:  y = (3/5)x - 3.  What happens if you multiply each term by 5, to eliminate the fraction?

5y = 3x - 3

Compare this to the second equation, 

5y - 3x = -10, or 5y = 3x - 10.

The coefficients of x and y (as 3 and 5 here) determine the slope of a straight line.  Since 5y = 3x is present in both equations, the two lines MUST be parallel.



y = 4
4y = 6   =>   y = 6/4

y+4 and y =3/2 are both horizontal lines.  Since they are horiz., they are parallel.


4 0
3 years ago
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