Exam 9: Understanding Sampling Distributions: Statistics As Random Variables

Use the following information for questions: Assume the cholesterol level in a certain population has mean $\mu$ = 200 and standard deviation $\sigma$ = 24. The cholesterol levels for a random sample of n = 9 individuals are measured and the sample mean $\overline{x}$ is determined. -What is the z-score for a sample mean $\overline{x}$ = 220?

Use the following information for questions: People who go on a (leisure) vacation tend to gain weight. It is thought that the average difference between weight before the vacation and after the vacation is roughly 2 pounds with a standard deviation of 2.5 pounds. Ten vacationing people are to be randomly selected and their weights measured, both upon departure and return of their vacation. -What is the standard deviation of the sampling distribution of the sample mean difference between after and before vacation weight?

Which of the following is not a z-score?

Use the following information for questions: A candy factory makes 20% (p = 0.20) of all its candies with chocolate liquor. A random sample of n =100 candies is taken, and $\hat{p}$ = proportion of candies in the sample made with chocolate liquor is calculated. -What is the z-score for $\hat{p}$ = 0.25?

Use the following information for questions: In a pond with a large population of turtles, the percent of three different types of turtles are presented in the table below. A random sample of 100 turtles is taken from the pond. -What is the standard deviation for the sample proportion of snapping turtles?

Use the following information for questions: Management of an airline uses a normal distribution to model the value claimed for a lost piece of luggage on domestic flights. The mean of the distribution is $600 and the standard deviation is $85. Suppose a random sample of 65 pieces of luggage is to be selected. -What is the probability that the average claimed value of the 65 pieces is over $625?

Use the following information for questions: College students spend a lot of their money, not on things they would like to buy, but on text books. College text books have increased in price significantly over the past few years. The amount students spend on text books is approximately normally distributed with a standard deviation of $50. The average amount spent on books each semester is $340 for undergraduate students and $250 for graduate students. Independent random samples of 100 undergraduate students and 80 graduate students are to be selected and the average amount they spent on text books last semester is to be compared (undergraduate - graduate). -What is the expected value for the difference in sample means?

Explain what the term "statistical significance" means in hypothesis testing.

Use the following information for questions: Suppose that the weight of apples eaten by individual Americans each year can be described by a normal distribution with mean $\mu$ = 15 pounds and standard deviation $\sigma$ = 5 pounds per year. -For a random sample of n = 9 people, what is the z-score for a sample mean $\overline{x}$ = 18 pounds?

Use the following information for questions: Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. -What is the expected value of the sample mean speed in a random sample of n = 10 cars?

Use the following information for questions: When people get married for the first time, the husband is, on average, 2 years older than the wife. The standard deviation of the difference in age is roughly 2.5 years. Suppose it is reasonable to assume that the distribution of the difference in age between the husband and the wife is normal. Twelve recently married couples (all first marriages) are to be selected and the average difference in age is to be calculated. -What is the correct notation for the statistic of interest?

Use the following information for questions: A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie is to be compared with the mean pressure after the movie. In general, blood pressure increases by 5 points after watching something violent happening with a standard deviation of 7 points. -What is the standard deviation of the sampling distribution of the sample mean difference in blood pressure before and after watching a movie containing violence?

A fourth grade class of 28 students is given a standardized math test. The mean score of the boys is compared to the mean score of the girls. Which statistic is being studied?

Use the following information for questions: Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. -What is the standard deviation for the sample mean speed in a random sample of n = 100 cars?

Use the following information for questions: Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. -What is the standard deviation for the sample mean speed in a random sample of n = 10 cars?

Use the following information for questions: In each situation, indicate whether the value given in bold print is . -Dyscalculia is a learning disability involving innate difficulty in learning or comprehending mathematics. It is akin to dyslexia and can include confusion about math symbols. Dyscalculia can also occur as the result of some types of brain injury. Dyscalculia occurs in people across the whole IQ range and affects roughly 5% of all Americans.

The standard deviation of the sampling distribution for a sample mean depends on the value(s) of

Use the following information for questions: In a pond with a large population of turtles, the percent of three different types of turtles are presented in the table below. A random sample of 100 turtles is taken from the pond. -What is the standard deviation for the sample proportion of spotted turtles?

Use the following information for questions: A large company is making all of its employees take a stress test. Test scores on this stress test follow a normal distribution with a mean score of 3 and a standard deviation of 0.9. A random sample of 35 employees is to be taken. -What is the probability that the sample mean stress score is lower than 2.75?

Use the following information for questions: Suppose height of college students can be modeled by the normal distribution. We believe the mean of the normal distribution is 1.72 m. We randomly sample 18 students and find an average of 1.69 m and a standard deviation of 5 cm (= 0.05 m). -What is the value of the t-statistic?