Exam 6: Putting Statistics to Work

A hypothesis test is to be performed. State the null and alternative hypotheses. -Last month the mean waiting time at a bank was $8.4$ minutes. The manager has installed a new computer system and claims that people will no longer have to wait as long.

Find the mode(s)for the given sample data. -The blood types for 30 people who agreed to participate in a medical study were as follows. Find the mode of the blood types.

Provide an appropriate response. -Boxplots are graphs that are useful for revealing central tendency, the spread of the data, the distribution of the data and the presence of outliers. Draw an example of a box plot and comment on each of these characteristics as shown by your boxplot.

Find the standard score for the given data value. -A data value in the 46th percentile.

State whether you would expect the data set to be normally distributed. -Resting heart rates for adults

Provide an appropriate response. -Heights of gymnasts at a certain college are normally distributed. Which of the following are the most plausible values for the mean and standard deviation?

Identify the distribution as symmetric, left-skewed, or right-skewed. -Weights of new-born babies

Solve the problem. -The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score. Round your answer to the nearest tenth. 647 541 340 350 491 353 356 508 470 482

Provide an appropriate response. -Scores on a test are normally distributed. Which of the following statements is (are)plausible? A: Margo's score was in the 90th percentile and she got a C B: Helena's score was in the 40th percentile and she got an A C: Monica's score was in the 5th percentile and she failed D: Gale's score was in the 70th percentile and she got a D

State whether you think the difference between what occurred and what you would expect by chance is statisticallysignificant. -In 50 rolls of a die, you got 40 sixes.

Provide an appropriate response. -Can the sample variance ever be a negative number? If so, for what types of data? If not, why not? Can the sample variance ever be zero? If so, for what types of data? If not, why not? Explain your reasoning.

Construct a boxplot as requested. -The weights (in pounds)of 30 newborn babies are listed below. Construct a boxplot for the data set. 5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2 7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7

Provide an appropriate response. -Jenny is conducting a hypothesis test concerning a population mean. The hypotheses are as follows. Null hypothesis: population mean $=50$ Alternative hypothesis: population mean $>50$ She selects a sample and finds that the sample mean is $54.2$ . She then does some calculations and is able to make the following statement: If the population mean were 50 , the chance that the sample mean would have come out as big as $54.2$ or bigger is 0.3. Do you think that she should reject the null hypothesis? Why or why not?

Provide an appropriate response. -Of the mean, median, and mode, which take(s)into account the numerical size of all the data values?

A hypothesis test is to be performed. State the null and alternative hypotheses. -During one flu epidemic the proportion of adults nationwide who have come down with the flu is $8 \%$ . The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explainyour thinking. -Suppose that a state introduces a state income tax which will be at a flat rate of 3%. The state legislature wishes to estimate how much money they will receive in taxes, and to do this they need to know the average income of residents of the state. Which information would be most useful, the mean income, the median income, or the mode of the incomes? Why?

Provide an appropriate response. -Scores on a test are normally distributed. Which of the following statements is (are) plausible? A: Daniel had a standard score of $1.9$ and got an A B: Jon had a standard score of $0.7$ and got a D $C$ : Eric had a standard score of $- 1.6$ and got a $B$ D: Raul had a standard score of 0 and got a C

Use the 68-95-99.7 rule to solve the problem. -At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6?

Solve the problem. -The diameters of bolts produced by a certain machine are normally distributed with a mean of $0.30$ inches and a standard deviation of $0.01$ inches. What percentage of bolts will have a diameter greater than $0.32$ inches?

Explanation: -Which of the distributions has the greatest variation?