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Testing the Mean

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State the null and alternate hypothesis and set the level of ... Hypothesis Testing of the Mean When. s is Unknown Using the Ti-83. Press the STAT button ... – PowerPoint PPT presentation

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Title: Testing the Mean


1
Testing the Mean
  • Section 9.2

2
  • To test µ when s is known
  • State the null and alternate hypothesis and set
    the level of significance a
  • If you can assume that x has a normal
    distribution, then any sample size will work. If
    you cannot, then use a sample
  • size 30
  • Use information to calculate E using the z value
    or the TI-83 with a Z-test
  • If P-value a reject H0. If P-value gt a, then
    do not reject H0
  • State your conclusion in the context of the
    application.

3
(No Transcript)
4
  • H0 µ 41 and H1 µ gt 41
  • Compute E using Z test, s 35, n 40 and
    47.
  • P .1401 gt a .05
  • So, We do not reject H0.
  • Based on this test we conclude that the sunspot
    activity
  • during the Spanish Colonial Period was
    higher than the
  • long-term mean

5
  • To test µ when s is unknown
  • Take a sample of size n and calculate the sample
    mean and the sample standard deviation sx.
  • State the null and alternate hypothesis and set
    the level of significance a
  • If you can assume that x has a normal
    distribution, then any sample size will work. If
    you cannot, then use a sample
  • size 30
  • Use information to calculate P using the t value
    or the TI-83 with a t-test (Student's t test)
  • If P-value a reject H0. If P-value gt a, then
    do not reject H0
  • State your conclusion in the context of the
    application.

6
Hypothesis Testing of the Mean Whens is Unknown
Using the Ti-83
  • Press the STAT button
  • Move the cursor to TESTS and Select 2T-Test
  • Press Enter
  • Highlight Stats
  • Enter requested information µ0, Sx, x, n
  • Highlight the appropriate alternative hypothesis
  • µ? µ0 (Two Tailed), µgt µ0 (Right Tailed),
    µltµ0 (Left Tailed)
  • Highlight Calculate and press ENTER
  • Read t value and p probability of H0
  • If p ? we reject H0 and if p gt ? we do not
    reject H0

7
Using TI-83 with t test, we calculate P .0478 gt
a .01 We therefore, do not reject H0
8
So, based on the data, we cannot say that the
drug 6-mP provides a different average remission
time than the previous drug.
9
Use a 10 level of significance to test the claim
that the mean weight of fish caught in a lake is
2.1 kg (against the alternate that the weight is
lower). A sample of five fish weighed an
average of 1.99 kg with a standard deviation of
0.09 kg.
10
test the claim that the mean weight of fish
caught in a lake is 2.1 kg (against the alternate
that the weight is lower). ...
  • H0 ? 2.1
  • H1 ? lt 2.1
  • Enter Data In TI-83
  • Calculate p .02614 lt .1 (10)
  • We reject Ho

11
We conclude (at 10 level of significance) that
the true weight of the fish in the lake is less
than 2.1 kg.
12
H0 µ 41.7 H1 µ 41.7, a
.05 Using Z-Test (We know s) P .046 a
.05 We reject H0 At 5 significance there
is enough evidence to conclude that with the new
e-mail system the number of E-mails is different.
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