(90x)^6 can this be simplified further?
2 answers:
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Answer:
The 99% confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is
The population standard deviation is
From the question we are told the confidence level is 99% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
Generally 95% confidence interval is mathematically represented as
=>
=>
Answer:
a)
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425
b) For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:
Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425
Step-by-step explanation:
Information given
represent the sample mean for the cubic feets of households
represent the population standard deviation
sample size
represent the value to verify
represent the significance level
t would represent the statistic
represent the p value
Part a
We want to test that the mean consumption of water per household has decreased due to the campaign by the city council, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the deviation the statistic is given by:
(1)
The statistic is given by:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425
Part b
For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:
Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425