3) The national Cesarean delivery rate for a recent year was 32.2% (number of live births performed by Cesarean section). A random sample of 100 birth records from three large hospitals showed the following results for type of birth. Test for homogenity of proportions at a = 0.10. Cesarean NonCesarean Hospital A 44 56 Hospital B 22 78 i). Write the null and alternative hypotheses. ii). Write the matrix of expected values. iii). State a conclusion. Hospital C 42 58 ii). Give the value of and the p-value using a calculator.

A neurosurgeon believes that lesions in a particular area of the brain, called the thalamus, will decrease pain perception. If so, this could be important in the treatment of terminal illness that is accompanied by intense pain. As a first attempt to test this hypothesis, he conducts an experiment in which 16 rats are randomly divided into two groups of eight each. Animals in the experimental group receive a small lesion in the part of the thalamus thought to be involved with pain perception. Animals in the control group receive a comparable lesion in a brain area believed to be unrelated to pain. Two weeks after surgery, each animal is given a brief electrical shock to the paws. The shock is administered in an ascending series, beginning with a very low intensity level and increasing until the animal first flinches. In this manner, the pain threshold to electric shock is determined for each rat. The following data are obtained. Each score represents the current level (milli-amperes)…

A toll collector wonders if drivers are equally likely to choose each of the three lanes at his toll booth. He selects a random sample of 465 drivers that approach the booth when all three lanes are empty, so that the driver's choice isn't influenced by the cars already at the booth. The table below summarizes the data: Lane Left Center Right Number of drivers 137 159 169 Which of the following is an appropriate alternative hypothesis for addressing this question? Drivers are not equally likely to choose each of the three lanes O The observed number of drivers choosing each lane is equal. The observed number of drivers choosing each lane is different from the expected numbers. The proportion of drivers choosing each of the three lanes are equal. O The proportion of drivers choosing each of the three lanes are all different.

V Based on advancements in drug therapy, a pharmaceutical company is developing Resithan, a new treatment for depression. A medical researcher for the company is studying the effectiveness of Resithan as compared to their existing drug, Exemor. A random sample of 414 depressed individuals is selected and treated with Resithan, and 191 find relief from their depression. A random sample of 557 depressed individuals is independently selected from the first sample and treated with Exemor, and 213 find relief from their depression. Based on the medical researcher's study can we conclude, at the 0.05 level of significance, that the proportion p₁ of all depressed individuals taking Resithan who find relief from depression is greater than the proportion p₂ of all depressed individuals taking Exemor who find relief from depression? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in…