Testing of Hypothesis

Testing of Hypothesis, Hypothesis testing, Independent t test, Independent z test, Analysis of variance, ANOVA, Comparison tests

Important MCQs Hypothesis Testing Quiz 3

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The post is about MCQs Hypothesis Testing Quiz. There are 20 multiple-choice questions. The quiz covers the topics related to the basics of hypothesis testing, level of significance, test statistical, critical region, parametric, and non-parametric tests. Let us start with MCQs Hypothesis Testing Quiz.

Online MCQs about Hypothesis Testing with Answers

1. The following are percentages of fat found in 5 samples of each of the two brands of baby food:
A:    5.7, 4.5, 6.2, 6.3, 7.3
B:    6.3, 5.7, 5.9, 6.4, 5.1
Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream?

 
 
 
 
 

2. For testing the equality of several variances the appropriate test is

 
 
 
 

3. In testing the difference between two populations, it is possible to use

 
 
 
 

4. In hypothesis testing, type II error is represented by $\beta$ and the power of the test is $1-\beta$ then

 
 
 
 
 

5. To perform a run test for randomness the data must be

 
 
 
 

6. In statistical testing of the hypothesis, what happens to the region of rejection when the level of significance $\alpha$ is reduced?

 
 
 
 
 

7. Which of the following statements is correct

 
 
 
 
 

8. Since   $\alpha$= probability of Type I error, then $1 -\alpha$

 
 
 
 
 

9. A data analyst conducts a hypothesis test. They fail to reject the null hypothesis. What statement best describes their conclusion?

 
 
 
 

10. The average growth of a certain variety of pine trees is 10.1 inches in three years. A biologist claims that a new variety will have greater three-year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a standard deviation of 2.1 inches. The appropriate null and alternative hypotheses to test the biologist’s claim are:

 
 
 
 
 

11. In hypothesis testing, you need to conclude, and you fail to reject a null hypothesis, which is actually false. What type of error do they commit?

 
 
 
 

12. Which of the following is NOT correct?

 
 
 
 
 

13. In a statistical hypothesis test of equality of means, such as $H_0:\mu=10$, if $\alpha=5\%$

 
 
 
 
 

14. In testing of hypothesis, type-II error may be defined as:

 
 
 
 

15. In a one-sample hypothesis test of the mean, what are the typical options for the alternative hypothesis?

 
 
 
 

16. Suppose you conduct a hypothesis test and choose a significance level of 5%. You calculate a p-value of 3.3%. What conclusion should be drawn?

 
 
 
 

17. In testing the statistical hypothesis, which of the following statement(s) is false?

 
 
 
 
 

18. In testing the statistical hypothesis, which of the following statement(s) is false?

 
 
 
 
 

19. If a Chi-square goodness of fit test has 6 categories and an $N=30$, then the correct number of degrees of freedom is:

 
 
 
 

20. You conduct a hypothesis test, you need to conclude and commit a type II error. Which of the following statements accurately describes this scenario?

 
 
 
 

MCQs Hypothesis Testing Quiz with Answers

MCQs Hypothesis Testing Quiz
  • In hypothesis testing, type II error is represented by $\beta$ and the power of the test is $1-\beta$ then
  • In statistical testing of the hypothesis, what happens to the region of rejection when the level of significance $\alpha$ is reduced?
  • Which of the following is NOT correct?
  • In testing the statistical hypothesis, which of the following statement(s) is false?
  • In testing the statistical hypothesis, which of the following statement(s) is false?
  • In a statistical hypothesis test of equality of means, such as $H_0:\mu=10$, if $\alpha=5\%$
  • Which of the following statements is correct
  • The average growth of a certain variety of pine trees is 10.1 inches in three years. A biologist claims that a new variety will have greater three-year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a standard deviation of 2.1 inches. The appropriate null and alternative hypotheses to test the biologist’s claim are:
  • Since   $\alpha$= probability of Type I error, then $1 -\alpha$
  • The following are percentages of fat found in 5 samples of each of the two brands of baby food: A: 5.7, 4.5, 6.2, 6.3, 7.3 B:    6.3, 5.7, 5.9, 6.4, 5.1 Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream?
  • In hypothesis testing, you need to conclude, and you fail to reject a null hypothesis, which is actually false. What type of error do they commit?
  • You conduct a hypothesis test, you need to conclude and commit a type II error. Which of the following statements accurately describes this scenario?
  • Suppose you conduct a hypothesis test and choose a significance level of 5%. You calculate a p-value of 3.3%. What conclusion should be drawn?
  • In a one-sample hypothesis test of the mean, what are the typical options for the alternative hypothesis?
  • A data analyst conducts a hypothesis test. They fail to reject the null hypothesis. What statement best describes their conclusion?
  • In testing the difference between two populations, it is possible to use
  • In testing of hypothesis, type-II error may be defined as:
  • If a Chi-square goodness of fit test has 6 categories and an $N=30$, then the correct number of degrees of freedom is:
  • For testing the equality of several variances the appropriate test is
  • To perform a run test for randomness the data must be
MCQS Hypothesis Testing Quiz with Answers

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Important MCQs Testing Hypothesis 2

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The post is about the MCQs Testing Hypothesis. There are 20 multiple-choice questions covering topics related to non-parametric tests and assumptions, null and alternative hypotheses, level of significance, and test statistics. Let us start with MCQs Testing Hypothesis.

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MCQs Testing Hypothesis with Answers

MCQs Testing Hypothesis quiz with answers
  • The sign test is
  • The non-parametric equivalent of an unpaired samples t-test is
  • The Mann-Whitney U test is preferred to a t-test when
  • When using the sign test, if two scores are tied, then
  • The sign test assumes that the
  • When testing for randomness, we can use
  • The Runs test results in rejecting the null hypothesis of randomness when
  • Wilcoxon Rank-Sum test can be of
  • The Wilcoxon Rank-Sum test used to compare
  • The Wilcoxon Signed Rank test is used
  • Which of the following tests uses Rank Sums
  • Which of the following tests must be two-sided?
  • In testing for the difference between two populations, it is possible to use
  • In a Wilcoxon Rank-Sum test
  • The Spearman Rank-Correlation test requires that the
  • To perform a Runs test for randomness the data must be
  • Three brands of coffee are rated for taste on a scale of 1 to 10. Six persons are asked to rate each brand so that there is a total of 18 observations. The appropriate test to determine if three brands taste equally good is
  • Comparing the times-to-failure of radar transponders made by firms A, B, and C based on an airline’s sample experience with the three types of instruments one may use
  • Which of the following tests is most likely assessing this null hypothesis: The number of violations per apartment in the population of all city apartments is binomially distributed with a probability of success in any one trial of $P=0.3$
  • A data professional on a marketing team conducts a hypothesis test to compare the mean time customers spend on two different versions of a company’s website. To start, they state the null hypothesis and the alternative hypothesis. What should they do next?
Statistics MCQS Testing Hypothesis

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Important MCQs Hypothesis Testing 1

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The post is about MCQs Hypothesis Testing. There are 20 multiple-choice questions covering topics related to the basics of hypothesis testing, assumptions about one sample, two samples, and more than two sample mean comparison tests, significance level, null and alternative hypothesis, test statistics, sample size, critical region, and decision. Let us start with MCQs Hypothesis Testing Quiz.

Please go to Important MCQs Hypothesis Testing 1 to view the test

MCQs Hypothesis Testing with Answers

MCQs Hypothesis Testing Quiz with Answers
  • $1 – \alpha$ is the probability of
  • A parameter is a ———- quantity
  • If we reject the null hypothesis, we might be making
  • Herbicide A has been used for years in order to kill a particular type of weed. An experiment is to be conducted in order to see whether a new herbicide, Herbicide B, is more effective than Herbicide A. Herbicide A  will continue to be used unless there is sufficient evidence that Herbicide B is more effective. The alternative hypothesis in this problem is
  • Analysis of Variance (ANOVA) is a test for equality of
  • Which of the following is an assumption underlying the use of the t-distributions?
  • For t distribution, increasing the sample size, the effect will be on
  • The t distributions are
  • Condition for applying the Central Limit Theorem (CLT) which approximates the sampling distribution of the mean with a normal distribution is?
  • Which of the following is a true statement, for comparing the t distributions with standard normal,
  • What is the probability of a type II error when $\alpha=0.05$?
  • The critical value of a test statistic is determined from
  • The null hypothesis is a statement that is assumed to be true unless there is convincing evidence to the contrary. The null hypothesis typically assumes that observed data occurs by chance.
  • The ——– typically assumes that observed data does not occur by chance.
  • Which of the following statements describes the significance level?
  • What is the first step when conducting a hypothesis test?
  • A data professional conducts a hypothesis test. They discover that their p-value is less than the significance level. What conclusion should they draw?
  • What does a two-sample hypothesis test determine?
  • What is the null hypothesis of a two-sample t-test?
  • To conclude the null hypothesis, what two concepts are compared?
MCQs Statistics Hypothesis Testing Quiz

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Testing a Claim about a Mean Using a Large Sample: Secrets

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In this post, we will learn about “Testing a claim about a Mean” using a Large sample. Before going to the main topic, we need to understand some related basics.

Hypothesis Testing

When a hypothesis test involves a claim about a population parameter (in our case mean/average), we draw a representative sample from the target population and compute the sample mean to test the claim about population. If the sample drawn is large enough ($n\ge 30$), then the Central Limit Theorem (CLT) applies, and the distribution of the sample mean is assumed to be approximately normal, that is we have $\mu_{\overline{x}} = \mu$ and $\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}} \approx \frac{s}{\sqrt{c}}$.

Hypothesis Testing: Testing a Claim about a Mean Using a Large Sample

Testing a Claim about a Mean

It is worth noting that $s$ and $n$ are known from the sample data, and we have a good estimate of $\sigma_{\overline{x}}$ but the population mean $\mu$ is not known to us. The $\mu$ is the parameter that we are testing a claim about a mean. To have a value for $\mu$, we will always assume that the null hypothesis is true in any hypothesis test.

It is also worth noting that the null hypothesis must be of one of the following types:

  • $H_0:\mu = \mu_o$
  • $H_0:\mu \ge \mu_0$
  • $H_0:\mu \le \mu_0$

where $\mu_0$ is a constant, and we will always assume that the purpose of our test is that $\mu=mu_0$.

Standardized Test Statistic

To determine whether to reject or not reject the null hypothesis, we have two methods namely (i) a standardized value and (ii) a p-value. In both cases, it will be more convenient to convert the sample mean $\overline{x}$ to a Z-score called the standardized test statistic/score.

Since, we assumed that $\mu=\mu_0$, and we have $\mu_{\overline{x}} =\mu_0$, then the standardized statistic is:

$$Z = \frac{\overline{x} – \mu _{\overline{x}}} {\sigma_{\overline{x}} } = \frac{\overline{x} – \mu _{\overline{x}}} {\frac{s}{\sqrt{n}} }$$

As long as $\mu=\mu_0$ is assumed, the distribution standardized test statistics $Z$ is Standard Normal Distribution.

Example: Testing a Claim about an Average/ Mean

Suppose the average body temperature of a healthy person is less than the commonly accepted temperature of $98.6^{o}F$. Assume that a sample of 60 healthy persons is drawn. The average temperature of these 60 persons is $\overline{x}=98.2^oF$ and the sample standard deviation is $s=1.1^oF$.

The hypothesis of the above statement/claim would be

$H_0:\mu\ge 98.6$
$H_1:\mu < 98.6$

Note that from the alternative hypothesis, we have a left-tailed test with $\mu_0=98.6$.

Based on our sample data, the standardized test statistic is

\begin{align*}
Z &= \frac{\overline{x} – \mu _{\overline{x} } } {\frac{s}{\sqrt{n} } }\\
&=\frac{98.2 – 98.6}{\frac{1.1}{\sqrt{60}}} \approx -2.82
\end{align*}

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