Question

The heights of UNC sophomores are approximately normally distributed. The heights in inches of 8 randomly selected sophomores are shown below. Use these heights to find a 95% confidence interval for the average height μ of UNC sophomores. Give the endpoints of your interval to one decimal place.

72, 69, 70, 68, 70, 66, 75, 64

a) Use these heights to find a 95% confidence interval for the average height μ of UNC sophomores. Give the endpoints of your interval to one decimal place.

95% confidence interval: (  ,  )

b) Using the 8 data points above, conduct a test of following hypotheses at level of significance α=0.05:

H₀: μ = 67; H_a: μ > 67

Find the sample mean x, the sample standard deviation s, the appropriate t-statistic and p-value. Use Excel when necessary and give all answers to four decimal places.

Sample mean =  
Sample standard deviation =  
t =  

p=

Answer 1

n=8,

calculate the sample mean and sample standard deviation for given data

we get,

= 69.25 , s =3.4122

a)

c= 95%

fomula for confidence interval is

where tc is the t critical value for c=95% with df=n-1 = 8-1 =7

tc = 2.365

69.25−2.853 < < 69.25+2.853)

(66.397  < <  72.103)

We get confidence interval as (66.4 ,  72.1)

b)

α=0.05:

H0: μ = 67

Ha: μ > 67

using excel we get Sample mean and Sample standard deviation as follows

Sample mean ( ) = 69.25
Sample standard deviation (s) = 3.4122

formula for test statistics is

t = 1.8651

calculate p-value for two right tailed test with df = 7

using excel we get

P-Value = 0.0522

P = 0.0522

since ( P-value = 0.0522) > ( α =0.05)

Hence, Failed to reject the null hypothesis.