Question

(1 point) A random sample of n=70n=70 is taken from a population of values to test the statistical hypotheses

H0:μ=100 HA:μ≠100

The mean, median, and standard deviation of this sample were found to be:

X¯¯¯¯=99.98 X˜=100.01 S=10.65

(a) Find a 93% confidence interval for μ. To avoid rounding errors please use R-Studio and not tables. Use at least four decimal points for your lower and upper bounds.

Lower Bound =
Upper Bound =

Answer 1

Here we hve to find confidence interval for population mean (μ).

n = 70.

X̄ = 99.98

S = 10.65

Confidence interval = 93% (=0.93)

The confidence interval for μ :

where z is the z score nd since the sample size is quite big we can use z sccore instead of t score to find the interval.

Now, we will find confidence interval in R.

Therefore, Lower Bound = 97.6736

Upper Bound = 102.2864

Population mean (μ=100) lies within this interval, so we fail to reject the null hyothesis.