Question

QUESTION 9

1. 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

2. 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. What is the p-value associated with this test?

   		<0.0001
   		0.0057
   		0.0114
   		0.2119
   		0.4237
   		0.7881
   		0.9943
   		> 0.9999

3. 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. What is our conclusion?

   		Reject the null hypothesis, there is not sufficient evidence to suggest the mean levels are not as labeled.
   		Do not reject the null hypothesis, there is not sufficient evidence to suggest the mean levels are not as labeled.
   		Reject the null hypothesis, the mean levels are not as labeled.
   		Do not reject the null hypothesis, the mean levels are not as labeled.

4. The one sample tt-statistic for testing

   H0:μ=10H0:μ=10

   H1:μ≠10H1:μ≠10  

   From a sample of n=20n=20 at the α=0.05α=0.05 level should reject H0H0 if the absolute value of tt is greater than or equal to which of the following values? [Reference: Table B: t-Distribution Critical Values]

   SELECT ONLY ONE VALUE.

   		1.721
   		1.725
   		1.729
   		2.080
   		2.086
   		2.093

5. Use table B to find the critical value associated with a probability of 0.90 to its left and 5 degrees of freedom. [Reference: Table B: t-Distribution Critical Values]

   		1.156
   		1.440
   		1.476
   		1.533
   		2.015
   		2.132

Answer 1

9:

The test statistics is

z = 2.53

The p-value is

p-value = 0.0114

Reject the null hypothesis, the mean levels are not as labeled.

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Test is two tailed. Degree of freedom: df=20-1=19

Using t table, the critical value of t is 2.093.

--------------------

Degree of freedom: df=5-1=4

The critical value such that area to the left of t is 1.533.