In 2015, the average duration of long-distance telephone calls from a certain town was 9.4 minutes. A telephone company wants to perform a test to determine whether this average duration of long-distance calls has changed. Twenty calls, originating from the town, was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes. a) Using a 1% level of significance, Complete the following: i. Give the null and alternative hypothesis of this test. [2] ii. Determine the critical value(s) of this test. [2] iii. Compute the value of the test statistic. [2] iv. State the decision rule. [1] v. Give your decision based on the available sample evidence. [1] vi. Hence, state your conclusion. [2] b) Construct the 99% confidence interval for the population mean duration of the longdistance calls from the town. [4]
X- duration of telephon call now
H0: M(X)=9.4 - null hypothesis
H1:M(X) - alrernative hypothesis
We are usint t-test
Critical value
where T- is t-statics
-calculation in mathcad
Conclusion: T< therefore null hypothesi M(X)=9.4 is true
Statement about shanging average duration of telephone calls has no 99% confidence.
Let us consider condition of valiidity of H0
From it we have
Answer 99% confidence interval for average duration of telephone call is (0.25.109).
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