A hypothesis test for a population mean does not reject the null hypothesis. Which one of the following cannot be correct? 0 a. A type I error may have occurred. O b.The null hypothesis is true. 0 c. A type II error may have occurred. 0 d.The alternative hypothesis is false. 0 e. The null hypothesis is false. When comparing the N(O.1) distribution with the t1 0 distribution, which of the following is true? 0 a. They t1o distribution is right skewed while the N(0,1)distribution is symmetric. O b.They both have the same general shape but the t10 distribution has fatter tails than the N(0,1) distribution. 0 c. They both have the same general shape but the t10 distribution has skinnier tails than the N(O.1) distribution. O d.They t1o distribution is left skewed while the N(0,1) distribution is symmetric. When performing a one-sample hypothesis test for the mean. which of the following is most crucial when deciding between a Z-test and a t-test O a. Whether you know the population variance. 0 b.Whether you know the data is normally distributed. 0 c. Whether you know the data is independent. 0 d.Whether the central limit theorem is applicable. When working correctly. a gambling machine is set to pay out minor prizes 30% of the time it is used. Data is collected on 20 uses of the machine where it paid out minor prizes 10 times. The owner of the machine is concerned that it is now paying out minor prizes too often and has asked a statistician to investigate. Which of the following methodologies should the statistician use to assess whether the machine is paying out minor prizes too often? 0 a. Small sample binomial test. 0 b. One sample test of proportions. O c. Chi-squared test of independence. 0 d.Two sample paired test. A researcher into road safety is interested in performing a hypothesis test to compare the mean reaction time of female drivers to sudden dangers and the mean reaction time of male drivers to sudden dangers. He randomly selects 40 female drivers and 40 male drivers from the register of WA driver licences. He arranges the females' names alphabetically and uses this list to assign each female a number between 1 and 40. He does the same thing for the males. Indicate the correct test procedure and reasoning. O a. One-sample t-test. The researcher should compare the sample mean reaction time for the females against the population mean reaction time for the men. 0 b. Paired t-test. Since there are 40 males and 40 females. we can pair the two samples. 0 c. Independent samples t-test. There is no natural pairing between the two populations. 0 d. Paired t-test. Since the males and females have WA driver licences, and are hence dependent samples, they can be paired. 0 e. Either independent samples or paired t-test will work