# 10.4 Matched or paired samples  (Page 3/14)

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## Try it

A new prep class was designed to improve SAT test scores. Five students were selected at random. Their scores on two practice exams were recorded, one before the class and one after. The data recorded in [link] . Are the scores, on average, higher after the class? Test at a 5% level.

SAT Scores Student 1 Student 2 Student 3 Student 4
Score before class 1840 1960 1920 2150
Score after class 1920 2160 2200 2100

The p -value is 0.0874, so we decline to reject the null hypothesis. The data do not support that the class improves SAT scores significantly.

Seven eighth graders at Kennedy Middle School measured how far they could push the shot-put with their dominant (writing) hand and their weaker (non-writing) hand. They thought that they could push equal distances with either hand. The data were collected and recorded in [link] .

Distance (in feet) using Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7
Dominant Hand 30 26 34 17 19 26 20
Weaker Hand 28 14 27 18 17 26 16

Conduct a hypothesis test to determine whether the mean difference in distances between the children’s dominant versus weaker hands is significant.

Record the differences data. Calculate the differences by subtracting the distances with the weaker hand from the distances with the dominant hand. The data for the differences are: {2, 12, 7, –1, 2, 0, 4}. The differences have a normal distribution.

Using the differences data, calculate the sample mean and the sample standard deviation. ${\overline{x}}_{d}$ = 3.71, ${s}_{d}$ = 4.5.

Random variable: ${\overline{X}}_{d}$ = mean difference in the distances between the hands.

Distribution for the hypothesis test: t 6

H 0 : μ d = 0  H a : μ d ≠ 0

Graph:

Calculate the p -value: The p -value is 0.0716 (using the data directly).

(test statistic = 2.18. p -value = 0.0719 using

Decision: Assume α = 0.05. Since α < p -value, Do not reject H 0 .

Conclusion: At the 5% level of significance, from the sample data, there is not sufficient evidence to conclude that there is a difference in the children’s weaker and dominant hands to push the shot-put.

## Try-it

Five ball players think they can throw the same distance with their dominant hand (throwing) and off-hand (catching hand). The data were collected and recorded in [link] . Conduct a hypothesis test to determine whether the mean difference in distances between the dominant and off-hand is significant. Test at the 5% level.

Player 1 Player 2 Player 3 Player 4 Player 5
Dominant Hand 120 111 135 140 125
Off-hand 105 109 98 111 99

The p -level is 0.0230, so we can reject the null hypothesis. The data show that the players do not throw the same distance with their off-hands as they do with their dominant hands.

## Chapter review

A hypothesis test for matched or paired samples (t-test) has these characteristics:

• Test the differences by subtracting one measurement from the other measurement
• Random Variable: ${\overline{x}}_{d}$ = mean of the differences
• Distribution: Student’s-t distribution with n – 1 degrees of freedom
• If the number of differences is small (less than 30), the differences must follow a normal distribution.
• Two samples are drawn from the same set of objects.
• Samples are dependent.

the power of the test is
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Continuation of the last question.Assist the Hotel manager to determine the number of possible breakfast combinations that can be served, one from each category
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3x2x3
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Are you answering the last question?
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bias came in sampling due to
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how do you find z if you only know the area of .0808
construct a frequency distribution
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How to take a random sample of 30 observations
you can use the random function to generate 30 numbers or observation
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How we can calculate chi-square if observed x٫y٫z/frequency 40,30,20 Total/90
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find t value,if boysN1, ،32,M1,87.43 S1square,39.40.GirlsN2,34,M2,82.58S2square,40.80 Determine whether the results are significant or insignificant
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The heights of a random sample of 100 entering HRM Freshman of a certain college is 157 cm with a standard deviation of 8cm. test the data against the claim that the overall height of all entering HRM students is 160 cm. previous studies showed that
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Z=x-mu/ std dev
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the power of the test is
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find the mean of 25,26,23,25,45,45,58,58,50,25
add all n divide by 10 i.e 38
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A manufacturer estimates that 3% of his output of a small item is defective. Find the probabilities that in a sample of 10 items (a) less than two and (b) more than two items will be defective.
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use binomial distribution with parameter n=10, p= 0.03, q=0.97
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A researcher observed that four out of every ten of their products are normally defective. A total of 360 samples of the products were being tested. If the sample is normally distributed and 220 of the products were identified to be faulty, test the hypothesis that the observation of the res
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please answer the ques"following values are obtained from life table T15=3,493,601 and e°15=44.6 then expected number of person alive at exact age 15 will be "
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make it clear
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how x minus x bar is equal to zero
When the mean (X bar) of the sample and the datapoint-in-context (X) from the same sample are the same, then it (X minus X bar) is equal to 0
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e.g. mean of. sample is 3 and one of the datapoints in that sample is also 3
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a numerical value used as a summary measure for a sample such as a sample mean is known as By By Sandhills MLT By OpenStax By Yasser Ibrahim By OpenStax By Vanessa Soledad By Jesenia Wofford By Danielrosenberger By Cath Yu By Melinda Salzer By Lakeima Roberts