1. Describing the Sampling Distribution of X¯. A manufacturer of automobile batt
ID: 3130925 • Letter: 1
Question
1. Describing the Sampling Distribution of X¯. A manufacturer of automobile batteries claims that the length of life for their batteries is normally distributed with a mean of 60 months and a standard deviation of 10 months (i.e. battery life N (60, 102 )). (a) Describe the sampling distribution of the sample mean for samples of size 16, i.e. describe the distribution of the average life time of these automobile batteries for samples of size 16. i. Shape (Choose one): • Normal • Approximately Normal • Not Normal ii. Mean: (Do NOT round answer.) iii. Standard Error: (Do NOT round answer.) (b) How would your answer in part (a) change if the battery life follows a skewed rght distribution? i. Shape (Choose one): • Normal • Approximately Normal • Not Normal ii. Mean: (Do NOT round answer.) iii. Standard Error: (Do NOT round answer.) (c) How would your answer in part (a) change if the battery life follows a skewed right distribution and the sample size was 64 instead of 16? i. Shape (Choose one): • Normal • Approximately Normal • Not Normal ii. Mean: (Do NOT round answer.) iii. Standard Error: (Do NOT round answer.)
Explanation / Answer
a) i) For small sample size, the distribution will be Normal. ii) mean=60 iii) standard error=sigma/sqrt n=2.5.
b. i) Not normal. ii) mean <60 iii)se<2.5
c. i) Not normalii) mean>60 iii)se>2.5
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