Answer questions and show work

NOTE: For each of the problems, you will need to identify if you are using:

• z-scores or t-scores. If the population standard deviation is given then you use z-score. If the sample standard deviation is given, then you use t-scores.
• One-tailed or two-tailed. If the direction is given, then it is one-tailed test.

Problem 1 (5 pts)

Researchers are interested in examining the effect of consuming 6 cups caffeine on response time in a driving simulator. The distribution of reaction for the population of individuals who have not consumes caffeine has a mean of ?=400 msec and ?= 40 msec. The researchers selected a sample of 36 participants. Every participant consumed 6 cups of caffeine and were test to identify the response time. The sample has a mean of M=392.

Are the data sufficient to conclude that caffeine has a significant effect on reaction? Use the standard six-step procedure an ?=0.05.

Problem 2 (5 points)

To evaluate the effect of a treatment, a sample is obtained from a population with a mean of ?= 75, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M= 79.6 If the sample consists of n =16 individuals with a standard deviation of s =12, are the data sufficient to conclude that the treatment significantly increased the mean with an ?= .05? use the standard six-step procedure

Problem 3 (10 points)

In a study, the population has a mean of ?=45 and a standard deviation ?= 16. The researchers selected a sample of n=16 participants. They administered the treatment and obtained a mean of M=52.

1. Can the researcher conclude that the treatment has a significant effect? Use the standard six-step procedure with an ?=0.05.
2. Can the researcher conclude that the treatment significantly increases the mean of the population? Use the standard six-step procedure with an ?=0.01.

Bonus (4 points)

A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of n=25 students is recruited to for the course and, at the end of the year, each student takes the SAT. The average score for this sample is M=562. For the general population, scores on the SAT are standardized to form a normal distribution with ?=500 and ?=100. Can the teacher conclude that students who take the course score significantly higher than the general population? Use the standard six-step procedure with an ?=0.01.