Answer:
Step-by-step explanation:
Let determine the angles behind each trigonometric expression:
Given that , the value of
is:
Given that , the value of
is:
The sine function of the sum of angles can be determined by the following identity:
If and
, then:
The 95% confidence interval based on the same data is 5.15 < μ < 6.05
Because it has a longer interval, the 95 percent confidence interval offers more details.
<h3>What is a confidence interval?</h3>The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.
Confidence intervals quantify how certain or uncertain a sampling technique is.
Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.
The 90% confidence interval is given by:
Mean - 1.645(S.D./) < μ < Mean + 1.645(S.D./
)
2μ = 5.22 + 5.98 = 11.2
μ = 11.2 / 2 = 5.6
Thus,
5.6 - 5.22 = 1.645(S.D./) = 0.38
S.D./ = 0.38 / 1.645 = 0.231
The 95% confidence interval is given by:
Mean - 1.96(S.D./) < μ < Mean + 1.96(S.D./
)
=5.6 - 1.96(0.231) < μ < 5.6 + 1.96(0.231)
= 5.6 - 0.4528 < μ < 5.6 + 0.4528
= 5.15 < μ < 6.05
The 95% confidence interval provides more information because it has a larger interval.
Learn more about confidence intervals here:
#SPJ4