A market researcher studied three background music conditions in a supermarket:  French accordion music, Italian string music, and no music.  Under each condition, the researcher recorded how many bottles of French, Italian, and other wine were purchased.  The table below summarizes the observed frequencies. The researcher wants to use the Chi-Square test to determine whether there is a relationship between background music and type of wine purchased. What are the degrees of freedom for this hypothesis test?

Computer programs are available that produce “random numbers” which are used in simulation studies of the sampling distributions of statistics.  One researcher used a computer program to generate 100 random single-digit integers (0 through 9) and tabulated the frequency with which each occurred. One concern is whether the computer program could be expected (in the “long run”) to produce equal numbers of each integer.             Suppose that the frequency with which each integer occurred was:                 Integer              0          1          2           3         4          5          6          7          8          9                 Frequency      12        10          9          8        10          7        13        11        11         9   What is the minimum value of the Chi-Square that would lead to the conclusion that the computer program was defective (that is, P-value < 0.05)?

What word is used to describe the distance at which light rays come together and are focused on one single point location? ©

28% of U.S. adults have experienced difficulty in making mortgage payments.  Forbes Magazine randomly sampled 400 adults from the “10 fastest dying cities in the U.S.” and found that 136 reported such difficulty. Forbes conducted a hypothesis test of whether the problem of making mortgage payments is different among adults in the 10 fastest dying cities in the U.S. than it is among all U.S. adults.  What is the value of the test statistic?

A music therapist studying relaxation was interested in whether the degree of relaxation in a stressful situation could be improved by listening to classical music.  To investigate the issue, the therapist obtained relaxation scores for ten participants who were about to take their Introductory Statistics final exam.  The participants then were asked to lie quietly on the floor of a carpeted room with their eyes closed, and listen to Beethoven’s Fifth Symphony.  After the music finished  playing, a second relaxation score was obtained for each participant.  The results are summarized in the table below.  Note: Higher scores indicate greater relaxation. After MusicRelaxation (A) Before Music Relaxation (B) Difference(A – B) n 10 10 10 Mean 15.8 14.4 1.4 SD 1.9 2.2 1.5 Which of the following represents the appropriate standard error for testing the null hypothesis that the population mean difference is equal to zero?

(True or False) The higher an objects reflectance the higher its emissivity. ©

(True or False) The amount of time that a LiDAR pulse takes to go out, bounce off an object, and return to the sensor is used to calculate the objects distance away from the LiDAR. ©

A survey is planned, to estimate the percent of U.S. shoppers who pay with credit cards.  Prior surveys suggest that 54% of all U.S. shoppers pay with credit cards.  What is the minimum number of randomly selected shoppers we must survey in order to obtain a 95% confidence interval with a margin of error no bigger than 0.01?

A company that produces light bulbs advertises that the mean life expectancy of its bulbs is at least 750 hours.  The Consumers Union suspects that the mean life span of the light bulbs is in fact less than 750 hours.  If it can prove this is the case, it plans to bring charges against the company for false advertising.  An employee of the Consumers Union decides to investigate the mean life of the light bulbs produced by the company.  She selects a random sample of 30 of this company’s light bulbs, subjects them to normal use, and measures for each light bulb the number of hours until it burns out.  The results for the sample of 30 bulbs are:  Mean = 700 hours,  and SD = 160 hours. Suppose the estimated standard error of the sample mean is 25 hours (actually it is not).  For a test of the null hypothesis that the population mean life expectancy of the light bulbs is 750 hours, against the alternative that it is less than 750 hours, which of the following best describes the P-value?

The mean life expectancy of U.S. adults is 77 years.  ABI Insurance Company wants to determine whether its policyholders have a mean life expectancy that exceeds that of U.S. adults.  A random sample of 20 ABI policyholders had a mean life expectancy of 78.6 years and a standard deviation of 4.48 years.  What are the appropriate null and alternative hypotheses in this situation?