Stat 2000 Statistics

A candy manufacturer sells boxes of its candy with an advertised weight of 50 grams. Weights of candy per box are known to follow a normal distribution with standard deviation 2.2 grams. A random sample of five boxes has a mean weight of 51.8 grams. We conduct a hypothesis test to determine if there is evidence that the true mean weight of all boxes of candy differs from the advertised weight. The P-value for the appropriate test of significance is: (A) 0.0336 (B) 0.0427 (C) 0.0548 (D) 0.0672 (E) impossible to determine, since the level of significance is not given. 2. We will measure the speeds of a random sample of 40 cars driving on a highway, and conduct a hypothesis test at the 5% level of significance to determine whether the true mean speed of all cars driving on the highway is greater than the posted limit of 100 km/h. The population standard deviation of speeds is known to be 17 km/h. What is the probability of making a Type II Error if the true mean speed of all cars on the highway is actually 110 km/h? (A) 0.0188 (B) 0.0274 (C) 0.0392 (D) 0.0446 (E) 0.0537 3. We would like to conduct a hypothesis test to determine whether the true mean rent amount for all one-bedroom apartments in Winnipeg differs from $850. We take a random sample of 50 one-bedroom apartments and calculate the sample mean to be $900. A 98% confidence interval for µ is calculated to be (830, 970). The conclusion for our test would be to: (A) fail to reject H0 at the 2% level of significance since the value 850 is contained in the 98% confidence interval. (B) fail to reject H0 at the 1% level of significance since the value 900 is contained in the 98% confidence interval. (C) reject H0 at the 1% level of significance since the value 850 is contained in the 98% confidence interval. (D) reject H0 at the 2% level of significance since the value 850 is contained in the 98% confidence interval. (E) fail to reject H0 at the 4% level of significance since the value 900 is contained in the 98% confidence interval. 4. The final percentage grades for a random sample of six students who failed a course (and had to repeat it) are shown below, for the first and second time they took the course. Some summary statistics are also provided. Student 1 2 3 4 5 6 mean std. dev. First Time (F