Solution 2.docx

Math 3339 EMCF Homework 8
Sections 7.2 - 7.3 & 7.7 - 7.9
Honework will NOT be accepted through email or in person. Homework must be submitted through
CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under
“EMCF” and choose ehw8.
1. For a fixed confidence level, when the sample size decreases, the length of the confidence interval for a
population mean decreases.
a. True
b. False
2. The z score corresponding to a 95 percent confidence level is 2.10.
a. True
b. False
3. The larger the level of confidence, the shorter the confidence interval.
a. True
b. False
4. A 90% confidence interval for a population parameter means that if a large number of confidence
intervals were constructed from repeated samples, then on average, 90% of these intervals would contain
the true parameter.
a. True
b. False
5. As the sample size increases, the confidence interval for the population mean will
a. decrease
b. increase
c. stay the same
d. decrease and then increase
6. Among 20 golden hamster litters recorded, there was a sample mean of x¯ = 7.72 baby hamsters, with a
sample standard deviation of s = 2.5 hamsters per liter. Create a 90% confidence interval for the mean
number of baby hamsters per liter.
a. 7.72 ± 0.9665
b. 7.72 ± 0.9196
c. 7.72 ± 0.559
d. 7.72 ± 1.0957
e. 7.72 ± 2.5
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7. Which statement about a hypothesis test is true?
a. The alternative hypothesis says that the observed is due to chance.
b. With p-value = 0.0001 there is significance.
c. The test statistic is the probability of getting the observed value or extreme.
d. None of these are true.
8. Bags of a certain brand of potato chips claim to have a net weight of 12 ounces. Net weights actually
vary slightly from bag to bag and are normally distributed with mean µ. A representative of a consumer
advocated group wishes to see if there is any evidence that the mean net weight is less than advertised
and so intends to test the hypothesis H0 : µ = 12 against Ha : µ < 12. To do this, the representative
selects 16 bags of this brand at random and determines the net weight of each bag. The sample mean
is x¯ = 11.98 and the sample standard deviation is s = 0.2. Calculate the test statistic.
a. z = -0.4
b. t = -0.1
c. t = -0.4
d. z = -0.1
e. t = 0.01
9. The hypothesis being tested is the ______________.
a. P-value
b. Level of significance
c. Null hypothesis
d. Alternate hypothesis
e. None of these
10. A t test is used instead of a z test because
a. the population standard deviation is known.
b. the population mean is known.
c. the population mean is unknown.
d. the population size is unknown.
e. the population variance is unknown.
f. None of these
11. The probability that we would get our observed result if the null hypothesis were true is the _______.
a. P-value
b. Level of significance
c. Null hypothesis
d. Alternate hypothesis
e. None of these
12. The one-sample t statistic for a test of H0 : µ = 10 vs. Ha : µ < 10 based on n = 10 observations has a
test statistic with the value t = −2.25. What is the p-value of this test?
a. 0.974
b. 0.026
c. 0.051
d. 0.255
e. none of these
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13. If the null hypothesis is rejected when it is true, a ______________ error has occurred.
a. Power
b. Type I
c. Type II
d. Type III
e. None of these
14. A one-sided significance test gives a p-value of .04. From this we can
a. Reject the null hypothesis with 99% confidence.
b. Reject the null hypothesis with 96% confidence.
c. Say that the probability that the null hypothesis is false is .04.
d. Say that the probability that the null hypothesis is true is .04.
e. None of these
15. Which of the following is not an assumption needed to perform a hypothesis test on a single mean using
a z test statistic?
a. An SRS of size n from the population.
b. Known population standard deviation, .
c. Either a normal population or a large sample (n ≥ 30).
d. The population must be at least 10 times the size of the sample.
e. All are needed.
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2.    *Water samples are taken from water used for cooling as it is being discharged from a power plant into a river.  It has been determined that as long as the mean temperature of the discharged water is at most 150̊ F, there will be no negative effects on the river’s ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge-water temperature above 150̊ , 50 water sample will be tank at randomly selected times, and the temperature of each sample recorded.

a.    Determine an appropriate null and alternative hypothesis for this test.
b.    In the context of this situation, describe type I and type II errors.
c.    Which type of error would you consider more serious? Explain.

3.    A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCI/L of radon.  The resulting readings were as follows:

105.6   90.9    91.2    96.9    96.5    91.3    100.1   105.0   99.6    107.7   103.3   92.4

Does this data suggest that the population mean reading under these conditions differs from 100?  Set up an appropriate hypothesis test to answer this question.
 

4.    In each of the following situations, for parts a – e write a short explanation of what is wrong and why.
a.    A researcher wants to test H0: 𝑥̅ = 30 versus the two sided alternative Ha: 𝑥̅ ≠ 30.
b.    A two-sample t statistic gave a P-value of 0.97.  From this we can reject the null hypothesis with
95% confidence.
c.    A manager wants to test the null hypothesis that average weekly demand is not equal to 100 units.
d.    The z statistic had a value of 0.014, and the null hypothesis was rejected at the 5% level because 0.014 < 0.05.
e.    Suppose the P-value is 0.03.  Explain what is wrong with stating, “The probability that the null hypothesis is true is 0.03.”
f.    In terms of probability language, a P-value is a conditional probability.  Define the event D as “observing a test statistic as extreme or more extreme than actually observed.” Using the definition of a P-value, which of the two conditional probabilities represents a P-value:
i.    P(H0 is true | D)
ii.    P(D | H0 is true)