Since it is observed that I z I = 3.464 > 1.96 it is concluded that the null hypothesis is rejected.
Therefore we reject John's claim.
Here:
we can use 1 sample proportion test to check the claim of John
H₀ : p₀ = 0.4
H₁ : p₀ ≠ 0.4
Test statistic is
z = p - p₀/√p₀(1-p₀)n
Let X be the random variable denoting the number of heads.
Now p = X/n
= 8/50
= 0.16
p₀ = 0.4
1-p₀ = 1-0.4
= 0.6
z = -3.464
since it is observed that I z I = 3.464 > 1.96 it is concluded that the null hypothesis is rejected.
Therefore we reject John's claim.
Learn more about Null hypothesis here:
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Complete question:
The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be barx = 4.2 minutes and s = 2.0 minutes. If appropriate, find a 90% confidence interval for the true mean time (in minutes) that customers at this supermarket wait in a check-out line
Answer:
(3.699, 4.701)
Step-by-step explanation:
Given:
Sample size, n = 45
Sample mean, x' = 4.2
Standard deviation 
= 2.0
Required:
Find a 90% CI for true mean time
First find standard error using the formula:
Standard error = 0.298
Degrees of freedom, df = n - 1 = 45 - 1 = 44
To find t at 90% CI,df = 44:
Level of Significance α= 100% - 90% = 10% = 0.10
Find margin of error using the formula:
M.E = S.E * t
M.E = 0.298 * 1.6802
M.E = 0.500938 ≈ 0.5009
Margin of error = 0.5009
Thus, 90% CI = sample mean ± Margin of error
Lower limit = 4.2 - 0.5009 = 3.699
Upper limit = 4.2 + 0.5009 = 4.7009 ≈ 4.701
Confidence Interval = (3.699, 4.701)
The units are ordered smallest to largest from top to bottom:
Picometer (pm) = 1 x 10⁻¹² meters
Nanometer (nm) = 1 x 10⁻⁹ meters
Micrometer (um) = 1 x 10⁻⁶ meters
Millimeter (mm) = 1 x 10⁻³ meters
Centimeter (cm) = 1 x 10⁻² meters
Decimeter (dm) = 1 x 10⁻¹ meters
Meters (m) = 1 meter
Kilometers (Km) = 1 x 10³ meters
Answer:
Step-by-step explanation:
In a dilatation for find the new coordinates we have to multiply the initial value for the the scale factor
A’(-3, 12)
B’(9,6)
C’(-9,-3)
so the general rule is:
(x,y) -> (3x, 3y)
Simplify both sides of the equation
x/16−(x+2/8) = 2x/16 + −1/8x + −1/4 = 2
Distribute
1/16x + −1/8x + −1/4 = 2
(1/16x + −1/8x)+(−1/4) = 2
Combine Like Terms
−1/16x + −1/4 = 2
Add 1/4 to both sides.
−1/16x + −1/4 + 1/4 = 2 + 1/4
−1/16x = 9/4
Multiply both sides by 16/(-1).
(16/−1)*(−1/16x)=(16/−1)*(9/4)
x=−36
