# Recent questions in Significance tests

Significance tests

### To explain:Whether the samples are independent or dependent.

Significance tests

### Hypothesis Testing Review For each problem below, simply identify the null and alternative hypotheses. Use appropriate notation/symbols. You do not have to run any hypothesis tests, although it's good practice and I'll post answers for all of them. 1) A simple random sample of 44 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. 2) In 1997, a survey of 880 households showed that 145 of them use e-mail. Use those sample results to test the claim that more than 15% of households use e-mail. Use a 0.05 significance level.

Significance tests

### If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain.

Significance tests

### To state:The null and alternative hypothesis.

Significance tests

### To state:The null and alternative hypotheses.

Significance tests

### Find the slope of the regression. Find the t-statistic for testing the slope. Find the p-value for testing the slope.

Significance tests

### To explain:The purpose of the study.

Significance tests

### Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

Significance tests

### To describe:How would you test the representative's claim and also identify the type of the test.

Significance tests

### In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean: For a two-tailed hypothesis test with level of significance a and null hypothesis $$H_{0} : \mu = k$$ we reject Ho whenever k falls outside the $$c = 1 — \alpha$$ confidence interval for $$\mu$$ based on the sample data. When A falls within the $$c = 1 — \alpha$$ confidence interval. we do reject $$H_{0}$$. For a one-tailed hypothesis test with level of significance Ho : $$\mu = k$$ and null hypothesiswe reject Ho whenever A falls outsidethe $$c = 1 — 2\alpha$$ confidence interval for p based on the sample data. When A falls within the $$c = 1 — 2\alpha$$ confidence interval, we do not reject $$H_{0}$$. A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p, $$\mu1 — \mu_2,\ and\ p_{1}, - p_{2}$$. (a) Consider the hypotheses $$H_{0} : \mu_{1} — \mu_{2} = O\ and\ H_{1} : \mu_{1} — \mu_{2} \neq$$ Suppose a 95% confidence interval for $$\mu_{1} — \mu_{2}$$ contains only positive numbers. Should you reject the null hypothesis when $$\alpha = 0.05$$? Why or why not?

Significance tests

### To describe:It is possible that the given claim is true or not. To describe:The questions that should ask about how the data were collected.

Significance tests

### Critical Thinking: One-Tailed versus Two-Tailed Tests For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain.

Significance tests

### What is the decision at a 0.05 level of significance for each of the following tests? F(3, 26) = 3.00 Retain or reject the null hypothesis? F(4, 55) = 2.54 Retain or reject the null hypothesis? F(4, 30) = 2.72 Retain or reject the null hypothesis? F(2, 12) = 3.81 Retain or reject the null hypothesis?

Significance tests

### A company is marketing a new product they say works better than the traditional test tube. There is so much interest in the product that 30 different labs around the world are testing the claim that this product is actually better. If each study uses an alpha level (alpha) of .10, and if the null hypothesis is true (that the test tube isn't any better that the traditional one), how many of the hypothesis tests would we expect to incorrectly find statistical significance (that is, conclude that the new test tube is better, when it actually isn't)?

Significance tests

### For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject Hg while a two tilled test results in the conclusion to fail to reject Ho? Explain.

Significance tests

### To describe:How would you test the representative's claim and also identify the type of test.

Significance tests

### A. Look for the definitions of the following terms related to hypothesis testing. 1. Null Hypothesis 2. Level of Significance 3. Type I error

Significance tests

### For the same data, null hypothesis, and level of significance, if the conclusion is to reject $$H_{0}$$ based on a two-tailed test, do you also reject Ho based on a one-tailed test? Explain.

Significance tests