The sum of six less than a number and five more than the same number is 9. Find the number.
1 answer:
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Answer:
(a) Test statistics = -4.54
(b) P-value = 1.9999
(c) We conclude that the population mean is equal to 17.
(d) Critical values for the test statistic are -1.96 and 1.96 .
(e) Test statistics is less than -1.96 or more than 1.96 represent the rejection region.
Step-by-step explanation:
We are given that ;
Null Hypothesis, :
= 17 where,
= population mean
Alternate Hypothesis, :
17
Also, a sample of 40 provided a sample mean of 14.13 and the population standard deviation is 4 i.e.;
= 14.13
= 4 and n = 40
(a) The test statistics used here will be;
~ N(0,1)
Test statistics = = -4.54
(b) P-value = P(Z > -4.54) = P(Z < 4.54) = 1 - P(Z >= 4.54)
From seeing the z % table we observe that the p-value will be less than 0.99995 in one -tail but in two tail case it will be less than 1.9999 .
(c) At 5% level of significance, we will accept null hypothesis because p -value is more than the significance level so we conclude that population mean is equal to 17.
(d) Using significance level of 5%, the critical values for the test statistic are -1.96 and 1.96 .
(e) If our test statistics is less than -1.96 or more than 1.96, then it will lie in the rejection region and we reject null hypothesis.
And since our test statistics is less than -1.96, so we reject and conclude that population mean is not equal to 17.