M8 WPSA - Writing/Problem Solving Activity

#1 Roller Coasters The heights (in feet) of 36 randomly selected top-rated roller coasters are listed. Assume the population standard deviation is 71.6 feet. At a=0.05, is there enough evidence to reject the claim that the mean height of top-rated roller coasters is 160feet? 325 188 306 107 208 167 105 78 140 232 230 170 170 205 305 135 200 200 100 223 135 195 80 90 120 210 82 161 245 88 70 116 121 146 149 124

Complete parts a - e. Follow the directions above to use StatCrunch for parts b and c.

a) Write the claim mathematically and state the null and alternative hypotheses. b) Find the standardized test statistic using StatCrunch. Copy and paste the results into your answers. c) Find the P-value using StatCrunch. Copy and paste the results into your answers. d) Decide whether to reject or fail to reject the null hypothesis based on the P-value. Explain your answer. e) Interpret the decision in the context of the original claim.

#2 Fluorescent Lamps A fluorescent lamp manufacturer guarantees that the mean life of a fluorescent lamp is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random sample of 32 fluorescent lamps. The results (in hours) are listed. Assume the population standard deviation is 1850 hours. At a=0.11, do you have enough evidence to reject the manufacturer's claim?

8,800 9,155 13,001 10,250 10,002 11,413 8,234 10,402 10,016 8,015 6,110 11,005 11,555 9,254 6,991 12,006 10,420 8,302 8,151 10,980 10,186 10,003 8,814 11,445 6,277 8,632 7,265 10,584 9,397 11,987 7,556 10,380

Use StatCrunch to find the mean of the given sample data so that you can complete a hypothesis test. Copy and paste the results into your work for the beginning of this exercise. Now complete parts a - e.

a)Write the claim mathematically and state the null andalternative hypotheses. b) Find the critical value(s) and identify the rejection region(s) for this test.Include a sketch of the rejection regions (refer to the diagrams on page 370) and explain how you would find the critical values using the standard normal distribution table. c) Find the standardized test statistic z, showing your work "by hand" using the formula. d) Based on your answers to parts b and c, decide whether to reject or fail to reject the null hypothesis based on the rejection regions. Explain your answer. e) Interpret the decision in the context of the original claim.