Question

QUESTION 1

1. MIT Research on Pills (a) A study funded by the Massachusetts Institute of Technology (MIT) tested the notion that even when it comes to sugar pills, some people think a costly one works better than a cheap one. Researchers randomly divided 82 healthy paid volunteers into two groups. All the volunteers thought they would be testing a new pain reliever.

   One group was told the pain reliever they would be using costs $2.5 (expensive), and the other group was told it costs only 10 cents (cheap) a pill. In reality, the pills that they were about to take were simply sugar pills. The volunteers were given a light electric shock on the wrist. Then the volunteers were given a sugar pill, and a short time later they were shocked again. Of the volunteers who were told to take the expensive pill, 32 of the 41 said they felt less pain afterward. Of the volunteers who were told to take cheap pill, 25 of the 41 said they felt less pain afterwards.

   Let us denote the proportion of volunteers who said they felt less pain afterwards in the (supposedly) expensive pill group by P_E; and the proportion of volunteers who said they felt less pain afterwards in the (supposedly) cheap pill group by P_C.

   Set up the null and alternative hypothesis to try to prove that people think an expensive pill works better than a cheap pill. Recall that what the researcher wants to prove goes to the alternative hypothesis.

   		H_0: P_E – P_C <= 0 H1: P_E – P_C > 0
   		H_0: P_C – P_E <= 0 H1: P_C – P_E > 0
   		H_0: P_E – P_C < 0 H1: P_E – P_C >= 0
   		H_0: P_C – P_E < 0 H1: P_C – P_E >= 0

Answer 1

We want to test the claim that Expensive pill works better than a cheap pill.

Since, the researcher, what wants to prove, goes to the alternative hypothesis, so the alternative hypothesis will be Expensive_Pill - Cheap_Pill > 0.

Therefore, the appropriate hypothese will be:

H_0 : P_E - P_C <= 0

H_1 : P_E - P_C > 0

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