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AleksandrR [38]
2 years ago
11

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the

course. If we are testing at the 5% significance level to see whether the business school preparation course is effective in improving exam scores, our critical value is 1.895. We should reject the null if the test statistic is
Mathematics
1 answer:
natta225 [31]2 years ago
3 0

Answer: We should reject the null if the test statistic is greater than <u>1.895</u>.

Step-by-step explanation:

We assume the population to be normally distributed.

Given:  Sample size : n=8, which is asmall sample (n<30), so we use t-test.

We always reject the null hypothesis if the absolute t-value is greater than critical value.

Therefore, We should reject the null if the test statistic is greater than <u>1.895</u>.

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A line that crosses segment at right angles while dividing the segment in half is called
iren [92.7K]

The correct answer is:

A line that crosses segment at right angles while dividing the segment in half is called <u>a perpendicular bisector</u>

Step-by-step explanation:

A bisector is a line that divides a line segment in two equal parts. A perpendicular bisector is a line that is perpendicular to given line segment and passes through the mid-point of the line segment. It can also be said as that the line perpendicular to a line segment that divides the lines in half is called the perpendicular bisector.

The correct answer is:

A line that crosses segment at right angles while dividing the segment in half is called <u>a perpendicular bisector</u>

Keywords: Perpendicular, bisector

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8 0
2 years ago
fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed w
EastWind [94]

Answer:

The p-value obtained is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours

Step-by-step explanation:

Complete Question

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed with a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternative hypothesis that the mean is not equal to 700 hours, if a random sample of 30 bulbs has an average life of 688 hours. Use a P-value in your answer.

Solution

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the mean life of the fluorescent lights is 700 hours.

The alternative hypothesis will now be that the mean life of the fluorescent lights is significantly different from 700 hours.

Mathematically,

The null hypothesis is represented as

H₀: μ = 700

The alternative hypothesis is represented as

Hₐ: μ ≠ 700

To do this test, we will use the z-distribution because no information on the population standard deviation is known

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 688 hours

μ₀ = 700 hours

σₓ = standard error = (σ/√n)

σ = standard deviation = 45 hours

n = Sample size = 30

σₓ = (45/√30) = 8.2158383626 = 8.216

z = (688 - 700) ÷ 8.216

z = 1.46

checking the tables for the p-value of this z-statistic

Significance level = 0.05 (This is used when significance level isn't given)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for z = 1.46, at 0.05 significance level, with a two tailed condition) = 0.14429

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.14429

0.14429 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours.

Hope this Helps!!

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Ber [7]

Answer:

Step-by-step explanation:

If it is Tanya and 3 friends, there are 4 people in total. If they all contributed the saem amount, you would do 75/4= 18.75 dollars each

8 0
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Maka made $45,670 last year.
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You need the percentages to answer the question
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