Psychology 406 Assignment #7

1) Suppose that a sample of size 8 is randomly chosen from a normally distributed population with mean 24 and variance 9. The standardized value corresponding to each observed value is computed by subtracting 24 and dividing the result by 3. Let T denote the sum of the squares of the 8 standardized values, and find:

a) P(T ≥ 20.09)

b) P(2.73 < T < 5.07)

c) P(T > 2.18)

2) Suppose that the daily changes in the Dow-Jones Average of Industrial Stocks are normally distributed and that the change on any given day is independent of the change on any other day. A random sample of 81 daily changes is obtained, with sample mean .20 and sample variance (S^{2}) 1.50. Suppose also that a second sample is obtained, with a sample size of 25, a sample mean of .15, and a sample variance of 1.20 (S^{2}). Find a 90% confidence interval for σ^{2} based on

a) the first sample only

b) the second sample only

c) both samples (use the “pooling” formula and the approximation in Hays, p. 359, for large degrees of freedom)

3) An IQ test is given to a randomly selected group of 10 Freshman at a given university and also to a randomly selected group of 5 Seniors at the same university. For the Freshman, the sample mean is 120 and the sample variance (s^{2}) is 196. For the Seniors, the sample mean is 128 and the sample variance is 121 (s^{2}). Find a 95% confidence interval for the ratio of the variance of the Freshman population to the variance of the Senior population, e.g., \frac{σ_{F}^{2}}{σ_{S}^{2}} . Do you reject equality of the two variances at α = .05?