Question

A researcher investigates whether a new medication produces enough sedation to impair mental functioning. It is known that scores on a standardized test containing a variety of problem -solving tasks are normally distributed with μ = 64 and σ= 8. Higher scores on the tasks are associated with higher levels of mental functioning. A random sample of n = 12 subjects is given the drug and then tested. For this sample, the mean is M = 58. Does the drug impair mental functioning? Conduct a z test with α= .01, one tail.

1. calculate standard error

2. What is the critical value of z? (Enter the tabled value and watch the sign.)

3. Calculate the z statistic (round to 2 decimal places).

4. Complete the APA formatted statistic (round z and p to 2 decimal places; watch the sign of z).

Answer 1

Solution:

We are given

µ = 64

σ = 8

M = 58

n = 12

α = 0.01

Here, we have to use one sample z test for the population mean.

H0: µ = 64 versus Ha: µ < 64

This is a lower tailed or left tailed test. (One tailed test)

(1)

Standard error = σ/sqrt(n) = 8/sqrt(12) = 2.309401

(2)

Critical value = -2.3263

(by using z-table)

(3)

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (58 – 64)/[8/sqrt(12)]

Z = -2.5981

Z = -2.60

(4)

P-value = 0.0047

(by using z-table)

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence (Z=-2.60, P = 0.0047) to conclude that the drug impair mental functioning.