A researcher takes sample temperatures in Fahrenheit of 20 days from Minneapolis and 18 days from Cleveland. Use the sample data shown in the table. Test the claim that the mean temperature in Minneapolis is different than the mean temperature in Cleveland. Use a significance level of α=0.01. Assume the populations are approximately normally distributed with unequal variances. Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Minneapolis Cleveland 70.1 66.1 69.5 65.9 65.7 61 71.7 62.8 62 67.9 75.3 74.5 63.2 69.1 62 72.5 76.9 80.4 71.3 72.7 70.9 70.4 70.5 76.6 65.1 62.2 76.2 66.1 70.3 86 69.5 81 80.2 68.3 74.3 63.3 70.7 64.6 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.) HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic = ____________ p-value =________________ The p-value is ______________ The correct decision is to ____________ . The correct summary would be:_______________ the claim that the mean temperature in Minneapolis is different than the mean temperature in Cleveland.
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!
A researcher takes sample temperatures in Fahrenheit of 20 days from Minneapolis and 18 days from Cleveland. Use the sample data shown in the table.
Test the claim that the
Assume the populations are approximately
Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs.
| Minneapolis | Cleveland |
|---|---|
| 70.1 | 66.1 |
| 69.5 | 65.9 |
| 65.7 | 61 |
| 71.7 | 62.8 |
| 62 | 67.9 |
| 75.3 | 74.5 |
| 63.2 | 69.1 |
| 62 | 72.5 |
| 76.9 | 80.4 |
| 71.3 | 72.7 |
| 70.9 | 70.4 |
| 70.5 | 76.6 |
| 65.1 | 62.2 |
| 76.2 | 66.1 |
| 70.3 | 86 |
| 69.5 | 81 |
| 80.2 | 68.3 |
| 74.3 | 63.3 |
| 70.7 | |
| 64.6 |
The Null Hypotheses is: H0: μ1 - μ2 = 0
What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen
HA: μ1 - μ2
Based on these hypotheses, find the following. Round answers to 4 decimal places.
Test Statistic = ____________
p-value =________________
The p-value is ______________
The correct decision is to ____________ .
The correct summary would be:_______________ the claim that the mean temperature in Minneapolis is different than the mean temperature in Cleveland.
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