QUESTION 1 Which of the following statements about hypothesis testing are TRUE? [Select ALL that are TRUE.] the alternative hypothesis is accepted when the null hypothesis is rejected the probability of making a Type I Error and the probability of making a Type II Error both decrease when the sample size is increased a hypothesis test can conclude that there is sufficient evidence to reject the null hypothesis Type I and Type II Errors represent mistakes a statistician makes when performing statistical analysis, such as applying the central limit theorem when it is not justified the probability of making a Type | Error and the probability of making a Type II Error both decrease when the critical region is made smaller statistical hypotheses about population parameters are proven true or false with 100% certainty O the null hypothesis involves setting an unknowable population parameter EQUAL TO a claimed value a hypothesis test can conclude that there is sufficient evidence to accept the null hypothesis QUESTION 2 Match the possible results of a statistical hypothesis test to the appropriate category (a Type | Error, a Type II Error, or a Correct Decision). FAILING TO REJECT the null hypothesis when it is actually TRUE A. Type II Error FAILING TO REJECT the null hypothesis when it is actually FALSE B. Correct Decision REJECTION of the null hypothesis when it is actually TRUE C. Type I Error REJECTION of the null hypothesis when it is actually FALSE QUESTION 3 Match the descriptoins of real-world situations to the best type of hypothesis test for population mean, where the null hypothesis is A : M =/ . [Note there is one for each possible answer.] A public health expert is investigating if the concentration of a certain pollutant in the atmosphere exceeds a critical threshold. A. a two-tailed test where the alternate hypothesis is H : u # H. V A consumer would like to test if the lifetime of a light bulb is actually less than what is B. this does not involve a hypothesis test on a population mean claimed on the packaging The owner of a lumber company is concerned that a new cutting process is systematically C. a left-tailed test where the alternate hypothesis is H : H H. A homeowner who is experiencing fluctuating internet connection speeds wants to measure the variability in their at-home internet connection speed to show to their internet service providerQUESTION 4 A local village would like to test whether the true mean water consumption per household (which is assumed to be normally distributed) is greater than 300 gallonslday. A sample of 9 households were measured and found to have a sample mean of 316 gallons/day and sample standard deviation of 24 gallons per day. Which of the following hypothesis test is appropriate for this scenario? 0 a single-tailed z-test O a single-tailed ttest O a two-tailed Meet 0 a two-tailed z-test QUESTION 5 A local village would like to test whether the true mean water consumption per household (which is assumed to be normally distributed) is greater than 300 gallonslday. A sample of 9 households were measured and found to have a sample mean of 316 gallons/day and sample standard deviation of 24 gallons per day. Calculate the test statistic for the sample (eg. the t-value or z-value). QUESTION 6 A local village would like to test whether the true mean water consumption per household (which is assumed to be normally distributed) is greater than 300 gallonslday. A sample of 9 households were measured and found to have a sample mean of 316 gallons/day and sample standard deviation of 24 gallons per day. Using the distribution tables, nd the critical value for comparing the test statistic (e.g. the critical t-value or zvalue) at signicance level 0.05. QUESTION 6 A local village would like to test whether the true mean water consumption per household (which is assumed to be normally distributed) is greater than 300 gallons/day. A sample of 9 households were measured and found to have a sample mean of 316 gallons/day and sample standard deviation of 24 gallons per day. Using the distribution tables, nd the critical value for comparing the test statistic (e.g. the critical t-value or zvalue) at signicance level 0.05. QUESTION 7 A local village would like to test whether the true mean water consumption per household (which is assumed to be normally distributed) is greater than 300 gallons/day. A sample of 9 households were measured and found to have a sample mean of 316 gallons/day and sample standard deviation of 24 gallons per day. What is the result of the hypothesis test, with null hypothesis H0: [4 = 300, at significance level 0.05. O Reject the null hypothesis. Q Do not reject the null hypothesis 0 Accept the null hypothesis O The hypothesis test is invalid QUESTION 3 Which of the following is NOT TRUE about p-values? O The pvalue is the minimum level of signicance for a Type | Error to reject the null hypothesis. 0 The pvalue provides a precise quantitative measure for the the strength of the conclusion to a hypothesis test (whether rejecting the null hypothesis or failing to reject the null hypothesis). 0 The pvalue has an inverse relationship to the probabilty of a Type II Error, i.e. as p increases, [3 decreases. O The pvalue is calculated as the area under the test statistic distribution curve beyond the test statistic value