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Answer:
Hypothesis
Null hypothesis:
Alternative hypothesis:
Statistic
P value
The degrees of freedom are given by:
And the p value would be given by:
Conclusion
Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 3.5
Step-by-step explanation:
Information given
represent the sample mean
represent the sample deviation
sample size
represent the value to test
t would represent the statistic
represent the p value
System of hypothesis
We want to verify if the true mean is equal to 3.5, the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
Statistic
The statistic would be given by:
(1)
Replacing we got:
P value
The degrees of freedom are given by:
And the p value would be given by:
Conclusion
Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 3.5