A cereal manufacturer claims to include 18.7 ounces of cereal in each box, with a standard deviation of 0.2 ounces. A random sample of 25 boxes shows an average of 18.5 ounces. Which of the following statements is correct? A. The claim is likely untrue, according to a z-value of −5.
B. The claim is likely untrue, according to a z-value of −1.5.
C. The claim is likely true, according to a z-value of −5.
D. The claim is likely true, according to a z-value of −1.5.
My answers is C
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
If you are using level of significance of P < .05, Z > 1.96.
To determine which statement is correct, we need to calculate the z-value and compare it to the given statements.
The z-value can be calculated using the formula:
z = (x - μ) / σ
Where:
x is the sample mean,
μ is the population mean (claimed value), and
σ is the standard deviation.
Given:
x = 18.5 ounces,
μ = 18.7 ounces, and
σ = 0.2 ounces.
Let's calculate the z-value:
z = (18.5 - 18.7) / 0.2
= -0.2 / 0.2
= -1
Now let's compare the calculated z-value to the given statements:
A. The claim is likely untrue, according to a z-value of −5.
B. The claim is likely untrue, according to a z-value of −1.5.
C. The claim is likely true, according to a z-value of −5.
D. The claim is likely true, according to a z-value of −1.5.
The calculated z-value is -1. Comparing it to the given statements, we see that statement B, "The claim is likely untrue, according to a z-value of −1.5," is the closest match. However, since the calculated z-value is -1 and not -1.5, none of the given statements are a perfect match.
Therefore, the correct answer is None of the above, as none of the statements exactly match the calculated z-value.