PROBABILITY & STATISTICS S2

The cholesterol content of large chicken eggs is normally distributed with a mean of 200 milligrams and standard deviation 15 milligrams. What is the probability that the mean cholesterol content of a random sample of 25 of these eggs is less than 205 milligrams?

• 0.6304

• 0.9522

• 0.3696

• 0.0478

• 1.667

The weights of the animals in a population are normally distributed with variance 144. A random sample of 16 of the animals is taken. The mean weight of the sample is 200 pounds. Calculate the lower bound of the symmetric 90% confidence interval for the mean weight of the population.

• 129.44

• 196.15

• 194.12

• 195.07

In textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

• Normal Distribution

• Binomial Distribution

• Sampling Distribution

• Poisson Distribution

The level of significance is the

• Maximum allowable probability of Type II Error

• Maximum allowable probability of Type I Error

• Same as the confidence coefficient

• same as the probability of obtaining test results

In hypothesis testing, the hypothesis tentatively assumed to be true is

• the alternative hypothesis

• the null hypothesis

• either the null or the alternative

• None of these alternatives is correct.

Let X be a continuous random variable with density function 

      
Calculate  $P\left(\left|X-\frac{1}{2}\right|>\frac{1}{4}\right)$  

• 0.0521

• 0.1563

• 0.3125

• 0.5000

• 0.8000

In point estimation

• data from the population is used to estimate the population parameter

• data from the sample is used to estimate the population parameter

• data from the sample is used to estimate the sample statistic

• the mean of the population equals the mean of the sample

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem the 0.22 is

• a parameter

• a statistic

• the standard error of the mean

• the average content of colognes in the long run

A random sample of 40 items is taken from a normal population. The sample had a mean of 82 and a standard deviation is 26. Which is the appropriate 99% confidence interval for the population mean?

•  $82\pm2.576\times\sqrt{\frac{26}{40}}$  

•  $82\pm2.326\times\frac{26}{\sqrt{40}}$  

•  $82\pm2.576\times\frac{26}{\sqrt{40}}$  
  

•  $82\pm2.326\times\sqrt{\frac{26}{40}}$  

An inspector needs to learn if customers are getting fewer ounces of a soft drink than the 28 ounces stated on the label. After she collects data from a sample of bottles, she is going to conduct a test of a hypothesis. She should use

• a two tailed test

• a one tailed test with an alternative to the right

• a one tailed test with an alternative to the left

• either a one or a two tailed test because they are equivalent