It is known in a pharmacological experiment that rats fed with a particular diet over a certain period gain an average of 40 gms in weight. A new diet was tried on a sample of 20 rats yielding a weight gain of 43 gms with variance 7 gms2 . Test the hypothesis that the new diet is an improvement assuming normality

A study investigated the therapeutic effectiveness of mindfulness versus traditional cognitive behavioural therapy for people with anxiety. Twenty-four clients with diagnosed anxiety were randomly assigned to one of the two therapy types, where there were 12 in each group. After six sessions their anxiety levels were measured, where lower scores indicated lower levels of anxiety (mindfulness mean = 35; cognitive behavioural therapy mean = 42). The pooled variance is 16.636 What is the approximate value of the standard error of the difference? 1.67 1.59 2.54 2.78

An amusement park conducted an internal audit on the wait times of its customers for the park's rides during a summer weekend. The audit found that the wait times of customers for the Shooting Star ride had a population mean of 31.2 minutes with a population variance of 6.3 minutes The park's head executive has doubts about the audit's findings concerning the Shooting Star ride. He hires an inspector to check these findings. On a summer weekend, the inspector takes a sample of 12 people at random waiting in line for the Shooting Star. She records their wait times and finds that the sample mean is 33.1 minutes and the sample variance is 4.8 minutes 2 Fill in the blanks below with the proper notation for the population mean, the population variance, and the sample variance. 66°F Cloudy Population mean: (Choose one) = 31.2 minutes X Population variance: (Choose one) = 6.3 minutes 2 Sample variance: (Choose one) 2 = 4.8 minutes Continue 3 W E 5. D DIL R Q Search 5 G 7 G Y U H 8 X C V B N M…

Two groups of mice were injected with a measured amount of tumor pulp. The first group of 27 mice was given a high dosage of chemotherapy while the second group of 30 mice was given a low dosage of chemotherapy. After forty days, the first group had an average tumor size of 0.51cc with a variance of 0.10; the second group had an average tumor size of 0.64cc with a variance of 0.045. Were the tumor sizes of group 1 significantly smaller than those of group 2? What is the observed test statistic?