Find the significance level of a one tailed test if the critical value of t is 2.264 and the sample size is 15. (write 2 decimal places)
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- If we conduct a z-test and use the alpha level of p < .05 [and our test is 'non directional,' i.e, we consider values at both ends of the z-score distribution] the value that we calculate for the z-test has to fall inside to be considered rare enough to be statistically significant. 5% of the lower values (tail of the curve) or 5% of the upper values in the other tail of the curve. The middle 5% of the curve 2.5% of the lower values (tail of the curve) or 2.5% of the upper values in the other tail of the curve. The middle 95% of the curveWe want to conduct a hypothesis test of the claim that the population mean score on a nationwide examination in biology is different from 506 . So, we choose a random sample of exam scores. The sample has a mean of 489 and a standard deviation of 78. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. , and it is from a non-normally distributed population with a known standard deviation of a. The sample has a size of 100 and it is from a non-normally distributed population with a known standard deviation of 78 z=? t=? it is unclear which statistics test to use? b. The sample has size 19, and it is from a normally distributed population with an unknown standard deviation. z=? t=? it is unclear which statistics test to use?Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations and you know that the paired-difference variable has a symmetric distribution that is far from normal. a. Is use of the paired t-test acceptable if the sample size is small or moderate? Why or why not?b. Is use of the paired t-test acceptable if the sample size is large? Why or why not?c. Is use of the paired Wilcoxon signed-rank test acceptable? Why or why not?d. If both the paired t-test and the paired Wilcoxon signed-rank test are acceptable, which test is preferable? Explain your answer.
- 4. Diastolic blood pressure for diabetic women has a normal distribution with unknown mean and a standard deviation equal to 10 mmHg. Researchers want to know if the mean DBP of diabetic women is equal to the mean DBP among the general public, which is known to be 76 mmHg. A sample of 10 diabetic women is selected and their mean DBP is calculated as 85mmHg. a. Conduct the appropriate hypothesis test at the 0.01 significance level. b. What would a Type-1 error in example setting be? c. How much power do you have to detect a difference of 11 mmHg between men and women?Only 12% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 351 randomly selected registered voters surveyed, 53 of them will vote in the upcoming election. What can be concluded at the αα = 0.01 level of significance? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer ≠ > = < (please enter a decimal) H1:H1: ? μ p Select an answer > ≠ < = (Please enter a decimal) The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject accept fail to reject the null hypothesis. Thus, the final conclusion is thatIn a sample of 1050 adults, it was found that 52% are registered to vote in their state. Use a 0.05 significance level to test the claim that less than 50% of all adults are registered to vote in their state.a. Find the test statistic.b. Find the critical value.c. Find the p-value.d. What is the conclusion about the null hypothesis (reject or fail to reject)?e. What is the final conclusion in nontechnical terms?
- A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. The most likely explanation is A) the placebo effect is present, which limits statistical significance. B) the sample size is small. C) that although the survival time has doubled, in reality the actual increase is really two years. D) the calculation was in error. The researchers forgot to include the sample size.A manufacturer of interocular lenses is qualifying a new grinding machine and will qualify the machine if there is evidence that the percentage of polished lenses that contain surface defects does not exceed 3%. A random sample of 300 lenses contains 8 defective lenses. Use α = 0.01. Suppose that the percentage of defective lenses is actually 2%. What is the β-error for this test? Suppose that a β-error of 0.05 is acceptable if the true percentage is 2%. What is the required sample size?A simple random sample of 300 items is selected from a large shipment, and testing reveals that 4% of the sampled items are defective. The supplier claims that less than 2% of the items in the shipment are defective. In order to determine the creditability of the supplier’s claim. The calculated value of the test statistic is -1.76. Determine the critical value of the test statistics at 1% level of significance
- Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is important. It is known that σ1 = σ2 = 1.0 psi. From a random sample of size n1 = 10 and n2 = 12, the values x̄1 = 162.5 and x̄2 = 155.0 are obtained. The company will not adopt Plastic 1 unless its mean breaking strength exceeds that of Plastic 2 by at least 10 psi. The P-value for the test H0: µ1 - µ2 = 10 versus H1: µ1 - µ2 > 10 is closest to:An investigator is interested if there is a difference in the time (in seconds) to sprint a given distance among non-smokers, past smokers and current smokers. He obtained the following data: 1. State your hypotheses. 2. What is the appropriate statistical test to determine if there is a difference in the sprint times among different smoking groups? 3. The investigator uses α = 0.01 as the level of significance (df = 2, 350). Give the critical value and region of rejection. 4. Should the null hypothesis be rejected? 5. State your conclusion. 6. Given your conclusion, what is the next procedure that should be done? 7. If the investigator classified the smoking groups according to their gender and obtained the mean sprint times per gender for each group, what type of statistical test should be used now?Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 11 having a common attribute. The second sample consists of 2200 people with 1546 of them having the same common attribute. Compare the results from a hypothesis test of p1=p2 (with a 0.05 significance level) and a 95% confidence interval estimate of p1-p2. Test Statistics is -1.49. Identify the critical value(s). (Round to three decimals) Test statistics in/not in the critical region. So, do we reject/fail to reject? Is there sufficient/not sufficient evidence? Since 0 is not included/included, does it indicate to reject/fail to reject the null hypothesis? The results are the same/not the same since the hypothesis test suggests p1 does equal/does not equal p2. and the confidence intervals suggest that p1 equals/not equal p2?
