Question

A sample of size 12, taken from a normally distributed population has a sample mean of 85.56 and a sample standard deviation of 9.70. Suppose that we have adopted the null hypothesis that the actual population mean is equal to 89, that is, H0 is that μ = 89 and we want to test the alternative hypothesis, H1, that μ ≠ 89, with level of significance α = 0.1.

a) What type of test would be appropriate in this situation?

i) A right-tailed test. ii) A left-tailed test. iii) A two-tailed test iv) None of the above.

b) What is the critical value? (for a two-tailed test give the
*positive value*). *For full marks your answer should be
accurate to at least two decimal places.*

*c*) What is the computed test statistic? *For full
marks your answer should be accurate to at least two decimal
places.*

d) Based on your test statistic and the decision rule you have
decided upon, what can we conclude about
*H*_{0}?

i) There is sufficient evidence, at the given significance
level, to reject *H*_{0}. ii) There is insufficient
evidence, at the given significance level, to reject
*H*_{0}; or we fail to reject
*H*_{0}. iii) There is insufficient evidence to make
it clear as to whether we should reject or not reject the null
hypothesis

Answer #1

Given that, sample size (n) = 12 sample mean = 85.56 and

sample standard deviation (s) = 9.70

The null and alternative hypotheses are,

H0 : μ = 80

H1 : μ ≠ 89

a) This hypothesis test is **two-tailed test.**

b) Degrees of freedom = 12 - 1 = 11

t-critical values at significance level of 0.1 with 11 degrees of freedom are, tcrit = ± 1.796

=> Critical value = **1.796**

c) Test statistic is,

=> Test statistic = t = **-1.229**

d) Decision Rule : Reject H0, if t < -1.796 OR t > 1.796

Since, test statistic = -1.229 > -1.796, we **fail to
reject H0.**

**Conclusion :** There is insufficient evidence, at
the given significance level; we fail to reject H0.

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