a)

For a particular brand of T.V. picture tube, it is known that the mean operating life of the tubes is 910 hours with a standard deviation of 35 hours. What is the mean and the standard deviation of the mean operating life for a random sample of size 81?It is stated that an email system takes on average 90 seconds to deliver a message. A user group complains that this value might not be accurate. The user group sets an experiment and found that a sample of 40 would provide with an average of 99 seconds and a standard deviation of 3. What are the null and alternative hypotheses for this test? O Ho : H = 3 Ha : H# 3 O Ho : # = 90 Ha : H # 90 O Ho : M = 40 Ha : # # 40 O Ho : H = 99 Ha : H # 99A manufacturer in steel rods considers that the manufacturing is working properly if the mean length of the rods is 3.5 inches. The population standard deviation of the length of the rods is unknown. The manufacture would like to see if the process is working correctly by taking a random sample of size 33 and doing a hypothesis test. What is the distribution of the test statistic for this test? 0 his O 1'31 0 N0]: 1) O Emmi?) O Nlms] Q mas, 33) All the children have been veryr naughty:r this vear, so Santa has decided to give them all coal for Christmas. Due to the human race using up coal like water, Santa is faced with the problem of a coal shortage. Santa has worked out that to make sure there is enough coal to go around, on average each child can get 4 grams of coal, so he got his elves to go about breaking up large chunks of coals into smaller bits. To see if there would be enough coal for each child, Santa took a sample of 9'5 chunks of coal. He found the coal had a sample mean weight of 3.91 grams with a standard deviation of 3.?3 grams. Since Santa is on top of his statistics course work, he decided to perform a t-test to test whether the true mean weight of his chunks of coal was 4 grams. 1v'll'hat degrees of freedom should Santa use for his reference t-distribution