Testing of Hypothesis

The quiz is about Testing of Hypothesis Quiz with Answers. The quiz contains 20 questions about hypothesis testing and p-values. It covers the topics of formulation of the null and alternative hypotheses, level of significance, test statistics, region of rejection, decision, effect size, value, confidence interval, about acceptance and rejection of the hypothesis. Let us start with the MCQs Testing of Hypothesis Quiz now.

Testing of Hypothesis Quiz with Answers

• The main goal of a direct replication is to ————-; replications are important according to Popper because —————.  
• What is an important reason to make sure the data and analysis scripts related to your research are well-organized?
• In Frequentist statistics, a p-value lower than the alpha level can mean —————. This differs from Bayesian statistics, which focuses on ——————.
• You performed 6 studies, only 4 of them had a significant result. The likelihood ratio of this happening assuming $H_0$ versus assuming $H_1$ tells you ————-. If you assume you had around 80% power, this likelihood ratio will probably show that ————-.
• We compare model A (the effect is 0) to model B (the effect is 1) and find a Bayes Factor of 10 which means ————–; the effect size is estimated with a certain 95% credible interval, this interval ———————.
• When $H_0$ is true, the probability that at least 1 out of an $X$ completely independent findings is a Type 1 error is equal to —————-, this probability ————— when you look at your data and collect more data if a test is not significant.
• You did a pilot study that found an effect size of 0.4, and $p < 0.05$. You decide to repeat the study with a power of 80% and an alpha of 5%. In the second study, assuming $H_0$ is true, the probability of a type 1 error is ————–. Assuming $H_0$ is false, the probability of a type 2 error is —————–.
• A researcher reports two significant findings testing the same hypothesis, using an alpha of 5%. The researcher predicted one finding before doing the study, but the other finding was observed during exploratory analyses where many tests were performed. Which statement is correct?
• An example of a standardized effect size is ————–; these are useful for ————–.
• If the difference between means is 2, and the standard deviation is 3, Cohen’s d is —————- which is ————— according to the rule of thumb.
• In an ANOVA with multiple predictors, a partial eta-squared gives ————–?
• You analyze your data in two ways. With Frequentist statistics you find a mean effect size of 3, with a 95% confidence interval of 1 to 5. With Bayesian methods, you find a mean of 2.75, with a 95% credible interval of 1.5 to 4. Which conclusions can you make?
• What are the benefits of performing a study with a larger sample size, compared to doing the same study with a smaller sample size (all else being equal)?
• You performed a p-curve analysis and found a skewed distribution of p-values with much more small p-values (around 0.01) than high p-values (around 0.04). What does this mean?
• You predict that your intervention will significantly increase participants’ performance on a test, this is an example of —————-. You find a significant result and conclude your theory is true, this is an example of ——————-.
• For confirmatory analyses it is problematic to —————; for exploratory analyses, it is NOT problematic to ——————.
• The main goal of direct replication is —————; the main reason(s) why successful replication rates are low is ——————-.
• How do we know there is publication bias in favor of significant results? Why is it unreasonable to expect articles with 4 experiments that aim for 80% power to exclusively show significant results?
• The Dutch Government wants 100% of scientific articles to be Open Access in 2024. What is the main advantage of open access that led the government to aim for 100% Open Access in 2024?
• If a test of hypothesis has a Type I error probability of 0.01, what does this mean?

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The quiz is about Hypothesis Testing MCQs with Answers. The quiz contains 20 questions about hypothesis testing and p-values. It covers the topics of formulation of the null and alternative hypotheses, level of significance, test statistics, region of rejection, decision, effect size, about acceptance and rejection of the hypothesis. Let us start with the Quiz Hypothesis Testing MCQs Quiz now.

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Online Hypothesis Testing MCQs with Answers

• You perform five tests without correcting for multiple comparisons. The error rate for each test is ————–. After using the Bonferonni correction, the individual error rate for each test is —————.
• An example of an unstandardized effect size is ——————; unstandardized effect sizes ——————.
• The difference between eta-squared and partial eta-squared is ————, the difference between eta-squared and omega-squared is ————–
• You replicate an older study, which reported both credible intervals and confidence intervals. You also calculate both. Which statement is correct?
• In studies with less observations, parameters like effect sizes vary —————, the power to detect the effect size in the population depends, among other things, on —————–.  
• You performed a p-curve analysis and found a skewed distribution of p-values which peaks around $p = 0.045$, what does this mean?
• You predict that your intervention will increase all participants’ performance on a test, this is an example of —————–. After the study, you conclude that the intervention only works for women but not men, this is an example of —————–.
• Predicting that a measured variable differs in two groups, without random assignment to conditions, is often ——————.
• Going through a dataset and looking at which effects are present can be problematic when —————-. It is NOT problematic when you ————–.
• What is the purpose of an ANOVA test?
• Which of the following is a possible alternative hypothesis $H_1$ for a two-tailed test?
• Using the teacher’s rating data, is there an association between native (native English speakers) and the number of credits taught? What test will you use?
• If I wanted to test for association using a chi-square test, whether there is an association between gender (Male or Female) and tenure-ship (tenured or not tenured), what would be my degree of freedom?
• Consider a normally distributed data set with mean $\mu = 63.18$ inches and standard deviation $\sigma = 13.27$ inches. What is the z-score when $x = 91.54$ inches?
• The battery life of smartphones is of great concern to customers. A consumer group tested four brands of smartphones to determine the battery life. Samples of phones of each brand were fully charged and left to run until the battery died. The table above displays the number of hours each of the batteries lasted. What test will be used to test the difference in means?
• A room in a laboratory is only considered safe if the mean radiation level is 400 or less. When a sample of 10 radiation measurements was taken, the mean value of the radiation was 414 with a standard deviation of 17. Some concerns mean radiation is above 414. Radiation levels in the lab are known to follow a normal distribution with a standard deviation of 22. We would like to conduct a hypothesis test at the 5% level of significance to determine whether there is evidence that the laboratory is unsafe. What will be the appropriate test?
• Which of the following statements about the ANOVA F-test score are true?
• An experiment has been performed with a factor having two levels. There are 10 observations at each level. The following data results: $\overline{y_1} = 10.5, S_1=2, \overline{y_2}=12.4, S_2=1.6$ You conduct a test of the hypothesis that the two means are equal. Assume that the alternative hypothesis is two-sided and that the population variances are equal. The P-value is:
• An experiment has been conducted to test the equality of two means, with known variances. The P-value for the Z-test statistic was 0.023. Assume a two-sided alternative hypothesis. The 95% confidence interval on the difference in the two means included the value zero.
• The most important assumption in using the t-test is that the sample data come from normal populations.

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Introduction to Types of Hypothesis Tests

In statistics, hypothesis tests are methods used to make inferences or draw conclusions about a population based on sample data. In this pose, we will discuss the Basic Types of Hypothesis Tests in Statistics. There are three basic types of hypothesis tests, namely (i) Left-Tailed Test, (ii) Right-Tailed Test, and (iii) Two-Tailed Test.

Note that I am not talking about Statistical tools used under specific conditions related to the data type and distribution. I am talking about the nature of the hypotheses being tested. Therefore, I will focus in this post on the area under the curve in the tails. In hypothesis testing, the distribution of the test’s rejection region can be characterized as either one-tailed or two-tailed. The one-tailed tests include both left- and right-tailed tests.

Left-Tailed Test

The left-tailed tests are used when the null hypothesis is being tested in a claim that the population parameter at least ($\ge$) a given value. Note that the alternative hypothesis then claims that the parameter is less than (<) the value. For example,

A tire manufacturer claims that their tires last on average more than 35000 miles. If one thinks that the claim is false, then one would write the claim as $H_o$, remembering to include the condition of equality. The hypothesis for this test would be: 
$$H_o:\mu\ge 35000$$
$$H_1: \mu<35000$$

One would hope that the sample data would allow the rejection of the null hypothesis, refuting the company’s claim.

The $H_o$ will be rejected in the case above if the sample mean is statistically significantly less than 35000. That is, if the sample mean is in the left-tail of the distribution of all sample means.

Right Tailed Test

The right-tailed test is used when the null hypothesis ($H_0$) being tested is a claim that the population parameter is at most ($\le$) a given value. Note that the alternative hypothesis ($H_1$) then claims that the parameter is greater than (>) the value.

Suppose, you worked for the tire company and wanted to gather evidence to support their claim then you will make the company's claim $H_1$ and remember that equality will not be included in the claim (H_o$). The hypothesis test will be

$$H_0:\mu \le 35000$$
$$H_1:\mu > 35000$$

If the sample data was able to support the rejection of $H_o$ this would be strong evidence to support the claim $H_1$ which is what the company believes to be true.

One should reject $H_o$ in this case if the sample mean was significantly more than 35000. That is, if the sample mean is in the right-tailed of the distribution of all sample means.

Two-Tailed Test

The two-tailed test is used when the null hypothesis ($H_o$ begins tested as a claim that the population parameter is equal to (=) a given value. Note that the alternative hypothesis ($H_1$) then claims that the parameter is not equal to ($\ne$) the value. For example, the Census Bureau claims that the percentage of Punjab’s area residents with a bachelor’s degree or higher is 24.4%. One may write the null and alternative hypotheses for this claim as:

$$H_o: P = 0.244$$
$$H_1: P \ne 0.244$$

In this case, one may reject $H_o$ if the sample percentage is either significantly more than 24.4% or significantly less than 24.4%. That is if the sample proportion was in either tail (both tails) of the distribution of all sample proportions.

Key Differences

• Directionality: One-tailed tests look for evidence of an effect in one specific direction, while two-tailed tests consider effects in both directions.
• Rejection Regions: In a one-tailed test, all of the rejection regions are in one tail of the distribution; in a two-tailed test, the rejection region is split between both tails.

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