Prove or disprove the following process is covariance stationary: (a) z, = (-1)' A, where A is a random variable with zero mean and unit variance?

Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: �"!= 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4.What is the variance of � "!

The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)

(e) Show that the sample mean of a simple random sample (drawn without replacement from a normal population) is dis- tributed normally with mean u and variance -² (1--=-1). n where N and n are population and sample sizes respectively. 4 In the 1 1 TI