You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 6% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places. Data available at StatKey, choose Mice Wgt Gain-2e data set
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 6% level of significance. Assume the population variances are unequal and that the weight changes are
Data available at StatKey, choose Mice Wgt Gain-2e data set
| Light (x1x1) | Dark (x2x2) |
|---|---|
| 1.71 | 2.27 |
| 4.67 | 2.53 |
| 4.99 | 2.83 |
| 5.33 | 4 |
| 5.43 | 4.21 |
| 6.94 | 4.6 |
| 7.15 | 5.95 |
| 9.17 | 6.52 |
| 10.26 | |
| 11.67 |
H0: μ₁ = μ₂
Ha: μ₁ > μ₂
Based on the hypotheses, find the following:
Test Statistic = __________ (Hint: difference in means from Ha)
p-value = ___________________
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