Hypothesis Testing — Unit test Answers

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?

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 textbook company states that the average time a student needs to take a quiz from its book is 30 minutes with a standard deviation of 3 minutes. A teacher using the book is not sure that this is correct for her classes and wants to check. She collects data on 10 random students and finds that the average time to take the quiz was only 25 minutes. As a result, the teacher performs a two-tailed hypothesis test with a significance level of 5%. Which conclusion is valid based on the results of the test?

The life spans of a computer manufacturer’s hard drives are normally distributed, with a mean of 3 years 6 months and a standard deviation of 9 months. What is the probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.230.59100.330.62930.670.74861.000.84131.330.90821.670.95252.000.9772

A normal distribution of data has a mean of 90 and a standard deviation of 18. What is the approximate z-score for the value 64?

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?

The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day?Probability DistributionDays Absent: XProbability: P(X)00.7810.1420.0330.014050.04

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?

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?

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?

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