A certain intelligence test has an N(100, 100) distribution. To see whether intelligence is inherited, tests are given to the eldest child o

Question

A certain intelligence test has an N(100, 100) distribution. To see whether intelligence is inherited, tests are given to the eldest child of each of a random sample of 16 acclaimed scholars. The average score of the children is 105. a. Give the null hypothesis to be tested. b. Give the alternative hypothesis. c. Perform the test. d. How likely is it that data like these represent a sample from a population in which the null hypothesis is true?

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Khoii Minh 4 years 2021-09-05T14:41:56+00:00 1 Answers 8 views 0

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  1. mit
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    2021-09-05T14:42:59+00:00
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    Answer:

    Follows are the solution to the given choices:

    Step-by-step explanation:

    In choice a:

    \to \mu = 100

    In choice b:

    \to \mu \neq 100

    In choice c:

    \to \ pop \ average=100 \\\\ \to \ variance \ of \ pop = 100 \\\\\to pop \ \ \sigma = \sqrt {(!00)} \\

                   = 10

    z= \frac{\bar x - \mu}{ \frac{\sigma}{\sqrt(n)}}\\\\

       =\frac{(105-100)}{\frac{10}{ \sqrt(16)}}\\\\=\frac{(5)}{ \frac{10}{4}}\\\\=\frac{5}{ \frac{5}{2}}\\\\= \frac{10}{5}\\\\=2

    \to p==2\times (1- \ righttail)\\\\\to \ righttail\ \ p = \text{NORM.S.DIST(2,TRUE)}

                            =0.977249868

    \therefore \\P=2 \times (1-0.9772)\\\\P=0.0455\\\\P<0.05 \\

    Null hypothesis to dismiss  

    Alternate solution assumptions embrace  

    There is really no valid proof at the 5% stage that  

    Knowledge is legacy

    In choice d:

    Possibly information such as this reflect a sample population with such a true p = 0.0455 meaning in the hypothesis  

    u is around 100.  

    11 +001

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