1. True or False. Justify for full credit.
(a) The normal distribution curve is always symmetric to 0. Hint: Where is the mean?
(b) If the variance from a data set is zero, then all the observations in this data set are identical. Hint: What does variance mean?
(c) P(AOR A complement) =1, where A complement is the complement of A. Hint: What does complement mean?
(d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis. https://onlinecourses.science.psu.edu/statprogram/node/138
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. http://statistics.wikidot.com/ch6
The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
100 + or - sd (15) = 1 sd =? 2 sds = ? 3sds = ?
2.. What is the probability that a randomly selected person has an IQ between 85 and 115?
3. Find the 90th percentile of the IQ distribution. Hint: Using a normal table, Probability = .4500
Z = 1.645 sd
4. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
standard deviation = sd/n
5. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit
xbar - 1.96 SD/SQRT(100) < mean < xbar +1.96 SD/SQRT(100) where xbar = sample mean
xbar = 3000 hours, SD = 500 hours, n = 100
Use for Questions 1 and 2: A grocery store takes a random sample of 200 customers. The average check-out time is 4 minutes with a standard deviation of two minutes.
1. The standard error of the mean is?
2. The 95% confidence level for the true average check-out time is?
3. A random sample of 244 observations has a mean of 10, a median of 12 and a mode of 33. The population deviation is known to equal 2.8. the 95.44% confidence interval for the population mean is?
4. The following random sample was collected: 22 33 44 6 The 80% confidence interval for the mean is?
5. A random sample of 200 people was taken. Sixty percent of the people favor President Obama. The 95% confidence interval for the true population of people who favor Obama is?