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Archy [21]
3 years ago
8

As part of quality control, a pharmaceutical company tests a sample of manufacturer pills to see the amount of active drug they

contain is consistent with the labelled amount. That is, they are interested in testing the following hypotheses:
H0:μ=100H0:μ=100 mg (the mean levels are as labelled)

H1:μ≠100H1:μ≠100 mg (the mean levels are not as labelled)

Assume that the population standard deviation of drug levels is 55 mg. For testing, they take a sample of 1010 pills randomly from the manufacturing lines and would like to use a significance level of α=0.05α=0.05.

They find that the sample mean is 104104 mg. Calculate the zz statistic.

−17.89−17.89

−8.00−8.00

−5.66−5.66

−2.53−2.53

−0.80−0.80

0.800.80

2.532.53

5.665.66

8.008.00

17.8917.89
Mathematics
1 answer:
ryzh [129]3 years ago
8 0

Answer:

The z statistic is 0.23.

Step-by-step explanation:

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 104 mg

population mean (mu) = 100 mg

sd = 55 mg

n = 10

z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find
mamaluj [8]

Answer:

x = 10. In other words, there number of girls is 10.

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

Rewrite to obtain:

\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}.

For this question:

\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}.

\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}.

Therefore:

\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

On the other hand, there are (15 + x) boys and girls in total. Using the formula for average:

\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}.

From the question, this average should be equal to 123. In other words:

\displaystyle \frac{1875 + 120\, x}{15 + x} = 123.

Solve this equation for x to obtain:

1875 + 120\, x= 123\, (15 + x).

(123 - 120)\, x = 1875 - 123 \times 15.

x = 10.

In other words, the number of girls here is 10.

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Step-by-step explanation:

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