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# Math quiz- need in one hour

1. Describe the properties of a Student’s t distribution, e.g. shape of distribution and degrees of freedom.2. Discuss the connections between a confidence level, margin of error, and the critical values.3. A 90% confidence interval for the mean of a given population is computed from a random sample and found to be .Based on this information, which of the following statements is true about this confidence interval?Select one:a. There is a 90% probability that is between 8 and 16.b. All of the above statements about confidence intervals are true.c. There is a 90% confidence that the true mean of the population is between 8 and 16.d. 90% of the values sampled are between 8 and 16.e. There is a 90% probability that the true mean of the population is 12 and a 90% probability that the true margin of error is 3.4. As the margin of error of a confidence interval increases, ___.Select one:a. the sample mean increases.b. the population standard deviation increases.c. the confidence interval decreases.d. the population standard deviation decreases.5. Based on the statement, “We are fairly sure that this new drug can eliminate headaches. Let’s put it on the market,” you have created the following null and alternative hypotheses:H0: The drug does not eliminate headaches.Ha: The drug does eliminate headaches.Which of the following is the Type I error associated with this scenario?Select one:a. We conclude that the drug does not eliminate headaches and it really does notb. We conclude that the drug does not eliminate headaches when it really doesc. We conclude that the drug eliminates headaches and it really doesd. We conclude that the drug eliminates headaches when it really does not6.Based on the statement, “We are fairly sure that this new drug can eliminate headaches. Let’s put it on the market,” you have created the following null and alternative hypotheses:H0: The drug does not eliminate headaches.Ha: The drug does eliminate headaches.Which of the following is the Type II error associated with this scenario?Select one:a. We conclude that the drug does not eliminate headaches and it really does notb. We conclude that the drug does not eliminate headaches when it really doesc. We conclude that the drug eliminates headaches when it really does notd. We conclude that the drug eliminates headaches and it really does7. In a hypothesis test, assuming the null hypothesis is true, the probability that the test statistic will take a value at least as extreme as the value actually observed is ___.Select one:a. the critical value of the test.b. the level of significance of the test.c. the p-value of the test.d. the margin of error of the test8.In hypothesis testing, the p-value tells us the ____ level of significance at which the null hypothesis can be ____.Select one:a. largest; acceptedb. smallest; rejectedc. smallest; acceptedd. largest; rejected9. In hypothesis testing, which of the following would be strong evidence against the null hypothesis?Select one:a. obtaining data with a large p-valueb. obtaining data with a small p-valuec. using a large significance leveld. using a small significance levele. none of the above is strong evidence against the null hypothesis10. Which of the following statements about rejecting the null hypothesis is true?Select one:a. If the sample data is such that for a one-tailed test of the mean you can reject H0 at the 5% level of significance, you can always reject H0for a two-tailed test at the 1% level of significance.Use the following scenario to answer questions #9 and #10.Based on the statement, “We are fairly sure that this new drug can eliminate headaches. Let’s put it on the market,” you have created the following null and alternative hypotheses:H0: The drug does not eliminate headaches.Ha: The drug does eliminate headaches.b. If the sample data is such that for a one-tailed test of the mean you can reject H0at the 1% level of significance, you can always reject H0 for a two-tailed test at the same level of significance.c. If the p-value is such that you can reject H0 for a 1% level of significance, you can always reject it for a 5% level of significance.d. If the p-value is such that you can reject H0 for a 5% level of significance, you can always reject it for a 1% level of significance.