Question

1.

Scientists studying the behavior of spiders have 12 orb spiders in their lab. Many orb spiders spin a new web each day. Does the amount of ambient light affect the size of the web? For each spider, the scientists measured the horizontal diameter (in mm) of the web spun under bright light conditions one day, and under low light conditions on a different day.

Here is the data:

spider	1	2	3	4	5	6	7	8	9	10	11	12
bright light	190	260	280	250	160	210	290	120	210	160	240	270
low light	170	170	160	120	170	240	120	180	200	100	160	330

The scientists verified the normality of the data. They are testing the null hypothesis that the mean diameter is the same under both lighting conditions, versus there is a difference. The test statistic for testing H₀: ? = 0 versus H_a: ? ? 0, where ? = ?_diff = ?_bright - ?_low, is _______________________ (give your answer to two decimal places)

2. In moderate intensity exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this target heart rate is approximately 120 bpm. An exercise physiologist designed a workout program for college students and is interested in knowing if the workout is as intense as intended.She used a simple random sample of fifty 20-year-old college students. Each participant did the workout routine wearing a heart rate monitor, and just before the “cool-down” portion of the routine, the heart rate for each participant was recorded. The sample mean was found to be 116 bpm with a standard deviation of s =9.3 bpm.

Is this routine “moderate intensity?”

Test the following hypotheses:

H₀ : ? = 120, H_a : ? < 120

The test statistic of this test is _______________________________ (give your answer to two decimal places).   

Answer 1