Testing of Hypothesis

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

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.

Online MCQs about Hypothesis Testing with Answers

1. 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

 
 
 
 

2. The sign test is

 
 
 
 

3. In a Wilcoxon Rank-Sum test

 
 
 
 

4. The Spearman Rank-Correlation test requires that the

 
 
 
 

5. 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?

 
 
 
 

6. To perform a Runs test for randomness the data must be

 
 
 
 

7. When testing for randomness, we can use

 
 
 
 

8. 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

 
 
 
 

9. Wilcoxon Rank-Sum test can be of

 
 
 
 

10. The Wilcoxon Signed Rank test is used

 
 
 
 

11. The sign test assumes that the

 
 
 
 

12. The Runs test results in rejecting the null hypothesis of randomness when

 
 
 
 

13. The Wilcoxon Rank-Sum test used to compare

 
 
 
 

14. The non-parametric equivalent of an unpaired samples t-test is

 
 
 
 

15. Which of the following tests must be two-sided?

 
 
 
 

16. The Mann-Whitney U test is preferred to a t-test when

 
 
 
 

17. When using the sign test, if two scores are tied, then

 
 
 
 

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

 
 
 
 

19. Which of the following tests uses Rank Sums

 
 
 
 

20. 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 $P=0.3$

 
 
 
 

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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