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Answer:
The 95% confidence interval for the difference in mean profile height and mean actual height of online daters is between 0.27 and 0.87 inches.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 30 - 1 = 29
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 29 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0452
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.57 - 0.3 = 0.27 inches.
The upper end of the interval is the sample mean added to M. So it is 0.57 + 0.3 = 0.87 inches.
The 95% confidence interval for the difference in mean profile height and mean actual height of online daters is between 0.27 and 0.87 inches.
Answer:
The sum is approximately 42.56
Step-by-step explanation:
Notice that you are dealing with a series whose first term is :
followed by sum of terms of the form:
and this is a geometric sequence of common ratio given by: (the value you need to multiply one term of the geometric sequence in order to find the following one)
Then, we can use the general formula for a partial sum of a geometric sequence for these last 5 terms for which m=5, the common ratio r = , and
= 3:
So, the total sum of the six terms is:
Total sum = 3 +39.5625 = 42.5625
which can be rounded to hundredth: 42.56