QUESTION 1 A tourism agency wants to know if the mean number of days spent by Australian tourists in Hong Kong has decreased from last year when the mean was 5.4 days. Let u denote the mean number of days an Australian tourist spends in Hong Kong. Which of the following is the alternative hypothesis the agency should be testing? 0 a. [J 5.4 OC.[JSS.4 Od.p25.4 QUESTION 2 A lunch bar has an average sales amount of $8.98. The manager initiates staff training to try to get them to sell more extras (chips, drinks etc), and after this training, a sample of 53 customers had the following sample statistics: ; = 9.32 and s = 2.98 Assume our question of interest is: "is there signicant evidence that the mean amount spent by customers has increased?" Calculate the observed value of the test statistic (correct to 2dp). QUESTION 3 A hypothesis test for a population mean is to be conducted based on a sample of size 25. What is the correct distribution for the test statistic (assume that the population variance is not known)? 0 a. t25 , since the sample size is small, and we need to assume that the population is normally distributed. 0 b. N(0,1), since the sample size is small we need to assume a normal distribution. QUESTION 3 A hypothesis test for a population mean is to be conducted based on a sample of size 25. What is the correct distribution forthe test statistic (assume that the population variance is not known)? 0 a. ['25 , since the sample size is small, and we need to assume that the population is normally distributed. @b. N(0,1), since the sample size is small we need to assume a normal distribution. 0 c. N(0,1), as the sample mean is normal by Central Limit Theorem. 0 d. {24 , since the sample size is small, and we need to assume that the population is normally distributed. QUESTION 4 A hypothesis test for a population mean has p-value 0.01. What is the decision at the 2.5% level of signicance? 0 3. Since p-value 0.025, we fail to reject the null hypothesis. QUESTION 5 A company makes new kale avoured energy drink and gives it to a sample of 50 people to try and then say whether they would buy it. Assume that it will only be protable to market this drink if more than 10% of people say they would buy it. Let p denote the population proportion of people who would buy the drink and assume the company is looking for eivdence that more than 10% of people will buy the drink. Which of the following is the alternative hypothesis the agency should be testing? 0 a- p 2 0.1 O b- p > 0.1 O C- p s 0.1 Od-;;: 0.05, we fail to reject the null hypothesis 0 b.8ince p-value 0.05, we accept the alternative hypothesis. 0 d.Since p-value > 0.05, we reject the alternative hypothesis. QUESTION 9 If a 1 tailed t-test gave a p-value of 0.04, what would be the p-value if we had run the test as a 2-tailed test? QUESTION 10 If I reject Ho when H0 is true, what sort of error have I made