Use the sample information x=44, o=6,n=17 to calculate the following confidence intervals for u assuming the sample is from population a) 95 percent confidence interval is from ____to_____ b) 99 percent confidence interval is from___to___
Use the sample information x=44, o=6,n=17 to calculate the following confidence intervals for u assuming the sample is from population a) 95 percent confidence interval is from ____to_____
b) 99 percent confidence interval is from___to___
Introduction:
The 100 (1 – α) % confidence interval for the population mean, μ, when the population standard deviation, σ is known, is as follows:
Here, n is the sample size, x̄ is the sample mean, and zα/2 is the critical value of the standard normal distribution, above which, 100 (α/2) % or α/2 proportion of the observations lie, and below which, 100 (1 – α + α/2) % = 100 (1 – α/2) % or (1 – α/2) proportion of the observations lie.
a.
The sample size is, n = 17.
The sample mean is, x̄ = 44.
The population standard deviation is given as, σ = 6.
The desired confidence level is 95%. Thus,
Using the above values, the required 95% is calculated as follows:
Thus, the required 95% confidence interval is from 41.1478 to 46.8522.
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