Question

The mean Verbal SAT score for the population of first students at Radford is 520. The standard deviation of scores in this population is 95. An investigator believes that the mean Verbal SAT of first year psychology majors is significantly different from the mean score of the population. The mean of a sample of 36 first year psychology majors is 548. Please test the investigator's prediction using an alpha level of .05. a. what is the null hypothesis?

b. one tailed or two tailed?

c. what is the alternative hypothesis?

d. what statistic should be used to test the null hhypothesis?

e. calculate the test statistic?

f. what is the decision?

Answer 1

Answer:

The mean score of population is equal to the mean score of psychology.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 520

Sample mean, $\bar{x}$ = 548

Sample size, n = 36

Alpha, α = 0.05

Population standard deviation, σ = 95

a),d) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 520\text{(Mean score of psychology is equal to the mean score of population)}\\H_A: \mu \neq 520\text{(Mean score of psychology is not equal to the mean score of population)}$

b)We use Two-tailed z test to perform this hypothesis.

d) Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

e) Putting all the values, we have

$z_{stat} = \displaystyle\frac{548-520}{\frac{95}{\sqrt{36}} } = 1.769$

Now, $z_{critical} \text{ at 0.05 level of significance } = 1.96$

Since,  

$z_{stat} < z_{critical}$

f) We accept the null hypothesis and reject the alternate hypothesis. Thus, the investigator's claim that mean score of psychology major is different from mean score of population is wrong. The mean score of population is equal to the mean score of psychology.