Prada Oracle 12.170 14.875 mean 1.056 2.208 std. dev. 10 12 n 20 df -2.7050 difference (Prada - Oracle) 0.7196 standard error of difference 0 hypothesized difference -3.76 t .0017 p-value (two-tailed) -4.2304 confidence interval 95% lower -1.1796 confidence interval 95% upper 1.5254 margin of error Interpret the results above (look up crticial values in our textbook): The previous table shows the results of this independent t test. At the .05 significance level, can you conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but who is unfamiliar with the t test for independent means. Will you reject the null or fail to reject it? How do you know?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were as follows: 9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle were as follows: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t test: two-sample assuming unequal variances.
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Hypothesis Test: Independent Groups (t test, unequal variance) |
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Prada |
Oracle |
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12.170 |
14.875 |
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1.056 |
2.208 |
std. dev. |
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10 |
12 |
n |
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20 |
df |
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-2.7050 |
difference (Prada - Oracle) |
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0.7196 |
standard error of difference |
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0 |
hypothesized difference |
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-3.76 |
t |
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.0017 |
p-value (two-tailed) |
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-4.2304 |
confidence interval 95% lower |
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-1.1796 |
confidence interval 95% upper |
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1.5254 |
margin of error |
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Interpret the results above (look up crticial values in our textbook): The previous table shows the results of this independent t test. At the .05 significance level, can you conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but who is unfamiliar with the t test for independent means. Will you reject the null or fail to reject it? How do you know?
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