Probability
Of the thirteen different women Calvin asks for a date, at least one of them accepts. Provide a written description of the complement of the given event.
What is at least one?
This is the one difference between a regular histogram and the corresponding relative frequency histogram.
What is the labeling of the y-axis with percentages?
A Type I error is the mistake of rejecting the following when it is actually true.
What is the null hypothesis?
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6 points, construct a 99% confidence interval for the mean score of all students.
91.68 < μ < 98.32
Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Determine which score is relatively better, the SAT score of 1490 or the ACT score of 17.0.
The SAT score of 1490 is relatively better than the ACT score of 17.0
Determine if the following are discrete data, continuous data, or not a random variable: exact weights of quarters now in circulation in the United States, shoe sizes of humans, political party affiliations of adults in the United States.
Identify which type of sampling is used. The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag.
What is a simple random sample?
Express the null hypothesis and the alternative hypothesis in symbolic form. A psychologist claims that at least 5.8 percent of the population suffers from professional problems due to extreme shyness.
p = 5.8% and p < 5.8%
Does the margin of error increase or decrease with an increased sample size? Does the margin of error increase or decrease with an increase in confidence level?
decreases; increases
Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z = -1.5. Find her temperature in degrees Fahrenheit.
97.27 degrees
A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets at least 3 successful first serves in? Assume that each serve is independent of the others.
92% chance of at least 3 successful first serves in.
This is what the absolute value of the linear correlation coefficient tells us about the scatterplot of the data.
How close are the points to being on a straight line?
The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by sigma equal to 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
Find the z score that is the critical value corresponding to a confidence level of 89.48%.
1.62
If z is a standard normal variable, find the probability that z lies between -2.41 and 0.
0.4920
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability that the given range of pounds lost is between 8 pounds and 11 pounds.
0.5
An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects ten schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? Simple random sample? Explain.
This is a random sample but not a simple random sample.
Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution (z distribution, t distribution, or neither of these) is used to test the claim that women have a higher mean resting heart rate than men?
t
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level: 98% confidence; the sample size is 800, of which 40% are successes.
0.0404
Mars, Inc. claims that 20% of its M&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 100.
The mean is 20 and the standard deviation is 4.
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
0.9608
This is the one calculation that does not apply to the interval level of measure.
What is taking a ratio?
Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find and interpret the P-value for the hypothesis test. n1=50, n2=50, x1=8, x2=7
The P-value of 0.7794 is the probability that, assuming the two population proportions are equal, we get sample data that are atleast as extreme as the given sample data.
Which critical value is appropriate for a 99% confidence level where n=17, sigma is unknown and the population appears to be normally distributed?
t = 2.921
The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6. Find the values of the mean and standard deviation after all test scores have been standardized by converting them to z-scores.
The mean is 0 and the standard deviation is 1.