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Hypothesis Testing Exercises: A Practical Guide to Statistical Inference, Assignments of Mathematics

A series of exercises designed to reinforce understanding of hypothesis testing concepts. It covers various scenarios involving hypothesis testing for proportions, means, and variances, providing practical applications of statistical inference. The exercises are suitable for students learning about hypothesis testing in statistics courses.

Typology: Assignments

2023/2024

Available from 12/18/2024

Milestonee
Milestonee 🇺🇸

4.4

(22)

3.5K documents

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WEEK 5 HOMEWORK
1.
In hypothesis testing the statistical conclusion is either to
reject or not to reject the null hypothesis based on the sample
data. Which of the following statements is true?
The conclusion will never reject a true null hypothesis.
The conclusion is always subject to error because it is
based on sample data.
The conclusion is always free from error if the correct
procedure is followed.
The conclusion will always reject a false null hypothesis.
2.
If a company wants to prove that the proportion (p) of its
revenues from overseas operations is more than 18%, the null
and alternate hypotheses are .
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one-tailed test
test of two sample means
test of two sample
proportions
two-tailed test
4.
The dean of a business school claims that the average
starting salary of its graduates is more than 85(in $000’s). It is
known that the population standard deviation is 10 (in $000’s).
Sample data on the starting salaries of 64 randomly selected
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H 0 : p = 0. 18 and H 1 : p >

  1. 18

WEEK 5 HOMEWORK

  1. In hypothesis testing the statistical conclusion is either to reject or not to reject the null hypothesis based on the sample data. Which of the following statements is true? The conclusion will never reject a true null hypothesis. The conclusion is always subject to error because it is based on sample data. The conclusion is always free from error if the correct procedure is followed. The conclusion will always reject a false null hypothesis.
  2. If a company wants to prove that the proportion ( p ) of its revenues from overseas operations is more than 18%, the null and alternate hypotheses are. H 0 : p = 0. 18 and H 1 : p
  3. 18 H 0 : p ≤ 0. 18 and H 1 : p > 0 .1 8 H 0 : p > 0. 18 and H 1 : p < 0. 18
  4. A^ test^ of^ the^ hypotheses,^ H 0 :^ p^ =^0.^18 and^ H 1 :^ p^ >^0.^18 is^ a . one-tailed test test of two sample means test of two sample proportions two-tailed test
  5. The dean of a business school claims that the average starting salary of its graduates is more than 85(in $000’s). It is known that the population standard deviation is 10 (in $000’s). Sample data on the starting salaries of 64 randomly selected

recent graduates yielded a

The value of the test statistic is -1.15 and fail to reject the null hypothesis .

  1. A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and a two-tailed test is +1.96. The observed z value from sample data is -1.85. The decision made by the researcher based on this information is to the null hypothesis. restate the null hypothesis change the alternate hypothesis into redefine fail to reject reject
  2. According to one survey taken a few years ago, 32% of American households have attempted to reduce their long- distance phone bills by switching long-distance companies. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 80 American households who have tried to reduce their long- distance bills. Suppose further that of these 80 households, 26% say they have tried to reduce their bills by switching long-distance companies. Is this result enough evidence to state that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? Let α = .01. (Round your answer to 2 decimal places.)
  3. According to Zero Population Growth, the average urban U.S. resident consumes 3.3 pounds of food per day. Is this figure accurate for rural U.S. residents? Suppose 64 rural U.S. residents are identified by a random procedure and their average consumption per day is 3.60 pounds of food. Assume a population variance of 1.31 pounds of food per day. Use a 5% level of significance to determine whether the Zero Population Growth figure for urban U.S. residents also is true for rural

U.S. residents on the basis of the sample data.

significance. Fifty-four of the messages were not business related. The appropriate decision is.

reject the null hypothesis gather more data increase the sample size fail to reject the null hypothesis maintain status quo

  1. The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m. to 10 a.m., Monday through Thursday. One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes. You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes. If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the appropriate decision is: increase the sample size reduce the sample size fail to reject the 7-minute average waiting time claim maintain status quo reject the 7-minute claim