At age 9 the average weight (21.3 kg) and the average height (124.5 cm) for both boys and girls are exactly the same. a random sample of 9-year-olds yielded these results. estimate the mean difference in height between boys and girls with 95% confidence. does your interval support the given claim?

a) Null hypothesis H₀: μ₁ = μ₂

Alternative hypothesis Hₐ: μ₁ ≠ μ₂

b) Critical is ±1.985523

c) The test statistic t is -0.1276

d) P-value > α = 0.05, we accept the null hypothesis

e) There is sufficient statistical evidence to suggest that the average weight of boys and girls are exactly the same

Step-by-step explanation:

a) Null hypothesis H₀: μ₁ = μ₂, the average weight of boys and girls are the same

Alternative hypothesis Hₐ: μ₁ ≠ μ₂ the average weight of boys and girls are not the same

b) Sample size, boys, n₁ = 60, girls, n₂ = 50

Mean height, boys, = 123.5 cm, girls, = 126.2 cm

Population variance, boys s₁ = 98, girls, s₂ = 120

The critical value at 95% confidence, degrees of freedom (smaller  between  n₁ and n₂) df = 50 - 1 = 49, α = (1 - 0.95)/2 = 0.025 the critical t is given from t relations as follows;

Critical = ±1.985523

c) For the test statistic, we have;

Plugging in the values where μ₁ = μ₂, we have;

The test statistic t = -0.1276

From t relations, we have the p-value , p = 0.8987748

d) Therefore, since the p-value > α = 0.05, we accept the null hypothesis

e) Based on the analysis, there is sufficient statistical evidence to suggest that the average weight of boys and girls are exactly the same.

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shell's the art director at her local community center. she paid $10 and for each child that attends she earns $4.

for each child she ears $4 that is the slope m = 4

she paid $10, that is the initial amount paid. so 10 is the y intercept b

m =4   and b = 10

y intercept is 10 so the point is (0,10)

we start graph from y intercept (0,10)

slope = 4 . we know slope = rise / run

slope = 4   or 4/1   are same

rise = 4   and run = 1

for rise we move 4 units up and for run we move 1 unit to the right

the graph is attached below

x axis is the number of child she attends

y axis is the amount   she earns