Given the following hypotheses: H0: μ ≤ 13H1: μ > 13 A random sample of 10 observations is selected from a normal population. The sample mean was 11 and the sample standard deviation 3.6. Using the 0.05 significance level:a) State the decision rule. (Round your answer to 3 decimal places.)State the decision rule________________b) Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.)Value of the test statistic ___________________

Question
Asked Nov 18, 2019
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Given the following hypotheses:

 

H0: μ ≤ 13

H1: μ > 13

 

A random sample of 10 observations is selected from a normal population. The sample mean was 11 and the sample standard deviation 3.6. Using the 0.05 significance level:

a) State the decision rule. (Round your answer to 3 decimal places.)

State the decision rule________________

b) Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.)

Value of the test statistic ___________________

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Expert Answer

Step 1
а.
Decision Rule:
Reject the null hypothesis (H) when the calculated test statistic value is greater than or
equal to the critical value. Otherwise, do not reject the null hypothesis.
That is, by using the t-distribution table, at a as 0.05, df as 9 and one tailed test.
cum. prob
one-tail
two-tails
df
t75
t so
0.50
0.25
0.20
0.15
0.10
0.05
0.20
1.00
0.50
0.40
0.30
0.10
0.000
1
1.000
1.376
1.963
3.078
6.314
2
3
0.816
0.765
0.000
1.061
0.978
0.941
1.386
1.250
1.190
1.886
2.920
2.353
2.132
1.638
0.000
0.000
0.741
1.533
0.000
0.727
0.920
1.156
1.476
2.015
6
7
8
9
10
0.000
0.000
0.000
0.718
0.711
0.906
0.896
0.889
1.134
1.943
1.440
1.119
1.415
1.895
1.860
1.108
0.706
1.397
0.000
0.703
0.700
0.883
1.100
1.383
1.833
0.879
0.000
1.093
1.372
1.812
Reject H when t 21.833
LO CO N CO
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а. Decision Rule: Reject the null hypothesis (H) when the calculated test statistic value is greater than or equal to the critical value. Otherwise, do not reject the null hypothesis. That is, by using the t-distribution table, at a as 0.05, df as 9 and one tailed test. cum. prob one-tail two-tails df t75 t so 0.50 0.25 0.20 0.15 0.10 0.05 0.20 1.00 0.50 0.40 0.30 0.10 0.000 1 1.000 1.376 1.963 3.078 6.314 2 3 0.816 0.765 0.000 1.061 0.978 0.941 1.386 1.250 1.190 1.886 2.920 2.353 2.132 1.638 0.000 0.000 0.741 1.533 0.000 0.727 0.920 1.156 1.476 2.015 6 7 8 9 10 0.000 0.000 0.000 0.718 0.711 0.906 0.896 0.889 1.134 1.943 1.440 1.119 1.415 1.895 1.860 1.108 0.706 1.397 0.000 0.703 0.700 0.883 1.100 1.383 1.833 0.879 0.000 1.093 1.372 1.812 Reject H when t 21.833 LO CO N CO

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