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kirill115 [55]
3 years ago
14

Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x overbarequals103

.29​, y overbarequals103.75​, requals0.899​, ​P-valueequals​0.000, and ModifyingAbove y with caret equals negative 9.5 plus 1.1 x​, where x represents the IQ score of the younger child. Find the best predicted value of ModifyingAbove y with caret given that the younger child has an IQ of 105​? Use a significance level of 0.05.
Mathematics
1 answer:
Lesechka [4]3 years ago
5 0

Answer:

106

Step-by-step explanation:

Given :

Number of the set of siblings = 20

This 20 pair yields $\overline x$ = 103.29, $\overline y$ = 103.75, requals = 0.899, P-value = 0.000

Let x represents the IQ score of the younger child.

And y is the predicted value of Y(^).

So according to the question,

x = 105

and y = -9.5 + 1.1 x

Then,

y = -9.5 + 1.1 (105)

y = -9.5 + 115.5

y = 106

So the best predicted value of Y(^) is 106

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The average expenditure on Valentine's Day was expected to be$100.89 (USA Today, February 13, 2006). Do male and femaleconsumers
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Answer:

(a) $62.16

(b) Male: $15.00

Female: $10.06

(c) Confidence Interval for male expenditure is ($106.40, $136.40)

Confidence interval for female expenditure is ($49.18, $69.30)

Step-by-step explanation:

(a) Male expenditure

Sample mean = $135.67, sd=$35, n=40, Z=2.576

Population mean = sample mean - (Z×sd)/√n = 135.67 - (2.576×35)/√40 = 135.67 - 14.27 = $121.40

Female expenditure

Sample mean= $68.64, sd=$20, n=30, Z=2.576

Population mean = 68.64 - (2.576×20)/√30 = 68.64 - 9.40 = $59.24

$121.40 - $59.24 = $62.16

(b) Male: Error margin = (t-value × sd)/√n

Degree of freedom = n-1 = 40-1= 39. t-value corresponding to 39 degrees of freedom and 99% confidence level is 2.708

Error margin = (2.708×35)/√40 = 94.78/6.32 = $15.00

Female

Degrees of freedom = n-1 = 30-1 = 29. t-value is 2.756

Error margin = (2.756×20)/√30 = 55.12/5.48 = $10.06

(c) Male

Confidence Interval (CI) = (mean + or - error margin)

CI = 121.4 + 15.00 = $136.40

CI = 121.4 - 15.00 = $106.40

Confidence Interval is ($106.40, $136.40)

Female

CI = 59.24 + 10.06 = $69.30

CI = 59.24 - 10.06 = $49.18

Confidence Interval is ($49.18, $69.30)

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