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?

Answer 1

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

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

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

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

                        $=0.977249868$

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

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