Hypothesis Testing — Unit test Answers

A city’s annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by . If the standard deviation of the city’s yearly rainfall totals is 1.8 inches, what is the city’s mean annual rainfall?

Weston completed a hypothesis test and found that he could not reject the null hypothesis. Which of the following is a valid reason for his conclusion?

Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500. With this average, the company can stay competitive with rates but not lose money. However, the statistician for the company believes that the cost of the average claim has increased. He pulled 40 recent claims and found the average to be $2,350. Which most restrictive level of significance would suggest that the company should raise rates? Upper-Tail Valuesa5%2.5%1%Critical z-values1.651.962.58

The grades of a science test are normally distributed. Thanh finds that his grade on the test has a z-score of –2.5. Which statement must be true?

The times taken to assemble a clock at a factory are approximately normally distributed with a given mean = 3 hr and standard deviation = 0.5 hr. What percentage of the times are between 2 hr and 4 hr?

A local newspaper compiles data on the number of days, X, people in a neighborhood receive the newspaper. The probability distribution for the data is shown in the table below. What is the probability that a randomly chosen person receives the newspaper at least one day per week?

A gymnastics coach records the scores of a gymnast and develops the probability distribution below. What is the probability the gymnast scores a 9 or 9.5?Probability DistributionGymnastics Score: XProbability: P(X)50.025.50.0260.066.50.170.167.50.1480.188.50.189?9.50.02

A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is , while the standard deviation is s. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58

Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

The proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485. What is the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.040.51600.210.58320.370.64430.380.64810.390.65171.000.8413

When finding the margin of error for the mean of a normally distributed population from a sample, what is , assuming a confidence level of 74%?

The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?

The set of life spans of an appliance is normally distributed with a mean = 48 months and a standard deviation = 8 months. What is the life span of an appliance that has a z-score of –3?

A researcher wants to survey people from different age groups to analyze voting patterns. Which type of survey will best accomplish this goal?

The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use?