Apsychologist is investigating the hypothesis that children who grow up as the only child in the household are more introvert than those who grow up in larger families. a sample of n = 30 only children (ie, who do not have siblings) is obtained and each child is given a standardized personality test. lower scores on this test indicate more introvert personality. for the general population, scores follow n(μ=50, σ=15). but the mean of these 30 only children is x = 40 .

is there enough evidence that suggests those who do not have siblings are more introvert than those who have siblings? carry out a hypothesis test using α = 0.10 .
(a) state the null hypothesis and alternative hypothesis.
(b) calculate the p-value. show your steps.
(c) what is your decision regarding the two hypotheses?

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true