The standard deviation for car battery lifetime is known to be 1.2 years. You ar
ID: 2921655 • Letter: T
Question
The standard deviation for car battery lifetime is known to be 1.2 years. You are interested in finding a 95% confidence interval for the mean lifetime of batteries when the car is driven primarily near the ocean. You test 40 cars and find that their battery's average lifetime is 5.3 years and the standard deviation is 1.7 years. Round your answers to two decimal places.
A. The sampling distribution follows a [ Select ] ["Chi-square", "t", "F", "Normal"] distribution.
B. With 95% confidence the mean battery life for all cars that are driven primarily near the beach is between [ Select ] ["5.96", "4.93", "4.52", "5.21"] and [ Select ] ["5.67", "5.86", "8.53", "6.32"] .
C. If many groups of 40 randomly selected cars that are primarily driven near the beach, then a different confidence interval would be produced from each group. About [ Select ] ["90", "95", "1", "5"] percent of these confidence intervals will contain the true population mean battery lifetime and about [ Select ] ["99", "1", "95", "5"] percent will not contain the true population mean battery lifetime.
Explanation / Answer
A. The sample size is large, n>30, and population standard deviation is known. Thus, the sampling distribution follows normal distribution.
B. The 95% c.i for population mean battery life for all cars that are driven primarily near the beach is: xbar+-z(sigma/sqrt n), where, xbar is sample mean, z is z critical at alpha/2 [(1-alpha)100=95, alpha=0.05, alpha/2=0.025], sigma is population standard deviation, n is sample size.
=5.3+-1.96(1.2/sqrt 40)
=(4.93, 5.67)
C. Per definition of confidence interval, if same population is sampled repeatedly with same sample size, and if confidence intervals are calculated every time, then 95% of the cases, the confidence interval will contain the true population mean. Thus, first option will be 95 and second option 5 (100-95).
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