What is nine? Huhhhhhhhhhhh?
2 answers:
Step-by-step explanation: The base of the power in the original equation becomes the base of the log. So we have .
Next, the exponent in the original equation goes on the other side of the equation and finally, the result in the original equation goes inside the log.
So we have
which is 3² = 9 written in logarithmic form.
This can also be switched around to read .
So the first choice will be your answer.
My work is also show in the image attached,
I just didn't switch it.
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Answer:
a) Null Hypothesis:
Alternative hypothesis:
b) The 95% confidence interval would be given by (910.05;959.95)
c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.
d)
Since is a bilateral test the p value is given by:
Step-by-step explanation:
a. State the hypotheses.
On this case we want to check the following system of hypothesis:
Null Hypothesis:
Alternative hypothesis:
b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x¯¯¯= 935?
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n=200 represent the sample size
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (910.05;959.95)
c. Use the confidence interval to conduct a hypothesis test. Using α= .05, what is your conclusion?
Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.
d. What is the p-value?
The statistic is given by:
If we replace we got:
Since is a bilateral test the p value is given by:
So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.
The value of b in the exponential function which is formed by Shanna for the price of land is 8% or 0.08.
<h3>What is percentage increase ?</h3>Percentage increase is the amount added to the initial value in the percentage part.
The value of a plot of land which is increases 8% every year has the current value of $350000.
The final value owner wants is $570000. Shanna writes an exponential function of the form, to model the value,v, of the land in t years as,
Here, in this exponential function the value of a is fixed or initial term which is $350000 and the value of b is the constant term which is change factor. Here, the value of b is 8%.
b=8%
b=8/100
b=0.08
Thus, the value of b in the exponential function which is formed by Shanna for the price of land is 8% or 0.08.
Learn more about the percentage increase here;
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