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Answer:
Since is a left sided test the p value would be:
Comparing the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly lower than 7.4 minutes at 10% of significance
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean i lower than 7.4, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by
(1)
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a left sided test the p value would be:
Conclusion
Comparing the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly lower than 7.4 minutes at 10% of significance