bluepanda21
23.11.2020 •
Mathematics
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Classkick
Mrs. Gallagher's car travels 24 miles for every gallon of gasoline it uses. How many gallons of gas would be required to make a 300 mile trip in her car
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Ответ:
12.5 or 12 and one half
Step-by-step explanation:
300/24=12.5
Ответ:
0.53187998
Step-by-step explanation:
We are given;
Population mean; μ = 60
Sample size; n = 25
Population standard deviation; σ = 4
Significance level; α = 0.01
Let's define the hypothesis;
Null hypothesis;H0: μ = 60
Alternative hypothesis;Ha: μ ≠ 60
Z-score for a significance level of 0.01 from tables is z = 2.575
Since it's a 2 sided test, then;
Z-score at lower limit = -2.575
Z-score at upper limit = 2.575
We know that z-score formula is;
z = (x¯ - μ)/(σ/√n)
At lower limit;
-2.575 = (x¯ - 60)/(4/√25)
-2.575 × 0.8 = x¯ - 60
-2.06 = x¯ - 60
x¯ = 60 - 2.06
x¯ = 57.94
At upper-limit;
2.575 = (x¯ - 60)/(4/√25)
2.575 × 0.8 = x¯ - 60
2.06 = x¯ - 60
x¯ = 60 + 2.06
x¯ = 62.06
the probability of a type II error is expressed as:
β = P(57.94 < x¯ < 62.06)
If the true average lifetime is 62 months, then;
β = P((57.94 - 62)/(4/√25)) < z < (62.06 - 62)/(4/√25)
β = P(-5.08 < z < 0.08)
β = P(Z < 0.08) - P(Z < -5.08)
From z-distribution table attached, we have; P(Z < 0.08) = 0.53188
Also, from z-distribution calculator online, we have;
P(Z < -5.08) = 0.0000000189
Thus;
β = 0.53188 - 0.0000000189
β ≈ 0.53187998