Question

1. A psychology researcher who does work in creativity wants to determine whether her sample of 50-year-old adults (N = 150) differs statistically from the population of 50-year-olds in intelligence. For her sample, she calculates the following: Mean = 109, SD = 10. (Hint: By definition, the mean IQ of this population is 100 and the population standard deviation is 15. Another hint: Use the z-test here!)
   1. Null hypothesis:
   2. Alternative hypothesis:
   3. Statistical test (You can’t miss this one!):
   4. Significance level (I’ll pick it for you; alpha = .05)
   5. Critical region for rejecting null hypothesis:
   6. Calculate the statistic (please show your work):
   7. Decision:

Answer 1

(A)

H0: Null Hypothesis: = 100

(B)

HA: Alternative Hypothesis: 100

(C)

Statistical test: Hypothesis test of one sample Z test of significance of population mean

(D)

Significance level = = 0.05

(E)

From Table, critical values of Z = 1.96

Reject H0 if Z < - 1.98 OR Z > 1.96

(F)

SE = /

= 15/

= 1.2247

Test statistic is given by:
Z = (109 - 100)/1.2247

= 7.3485

(G)
Since calculated value of Z = 7.3485 is greater than critical value of Z = 1.96, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that her sample of 50 - year - old adults (N = 150) differ statistically from the population of 50 - year - olds in intelligence.