Answer:
Mean is 83.7%
And, the standard deviation is 0.033
Step-by-step explanation:
The computation of the mean and the standard deviation is as follows:
Let us assume the P be the sample proportion
Mean is 83.7%
And, the standard deviation is
= 0.033
Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus .
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
.
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
,
where
For this confidence interval:
Hence the width of the 90% confidence interval is
.
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
.