Hypothesis Test of Mean
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Example: A sample of size 20 has a mean
of 110 and a standard deviation of 16.
Use the TI-83 calculator to test the hypothesis that the population
mean is greater than 100 with a level of significance of a =
5%.
Solution: “The population mean is greater than 100” means
the alternate hypothesis is H1: m > 100, and the null hypothesis is H0:
m £ 100.
Follow the steps below to solve the problem using the TI-83. [NOTE: If the p-value < a, reject the null hypothesis; otherwise, do not
reject the null hypothesis. |
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Press STAT and the right arrow twice to select TESTS. To select the highlighted
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Use right arrow to select Stats (summary values rather
than raw data) and Press ENTER. Press down arrow to select Calculate and press ENTER. |
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Results: Since the p-value is 0.0058, reject the null hypothesis
with an alpha value larger than 0.0058 (0.58% level of significance or
larger). |
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Hypothesis Test of Mean
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Example: Two samples were taken, one from
each of two populations. Use the
TI-83 calculator to test the hypothesis that the two population means are
equal with a level of significance of a = 2%.
Solution: For the two samples, we have the
following summary data:
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sx1 = 5
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sx2 = 7
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n1 = 8
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n2 = 5
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H0: m1 = m2
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H1: m1 ¹ m2
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Use a =
2%
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Press STAT and the right arrow twice to select TESTS.
Use the down arrow to select
4:2-SampTTest…
Press ENTER.

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Use right arrow to select Stats (summary values rather than raw data). Enter sample mean, standard deviation, and sample size for
samples 1 and 2. Press down arrow to select Calculate and press ENTER.
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Results: Since the p-value is 0.384, do not reject the null hypothesis
with an alpha value of 0.02 (because 0.384 is not less than 0.02). Conclude that the two population means are not different. |
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