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Answer:
Yes. The sample size is large enough
H0: μ=170
Ha: μ≠ 170
a) μ= 172.52
b) 10.31
c) yes, the data is distributed around both sides of the mean
d) H0: μ=170 is true
Step-by-step explanation:
a) mean= sum of all sample values/25
(170+167+174+179+179+187+179+183+179 +156+163+156+187+156+167+156+174+170+ 183+ 179+ 174+ 179+ 170+ 159+ 187)/25 = 172.52
b) standard deviation= √(∑(x-μ)²/25)
Using this formula value of standard deviation was computed to be 10.31
c) Least value is 156, difference between least and mean is 16.52
Max value is 187, difference between max and mean is 14.48
A scatter plot shows that number of values higher than mean is 14 and number of values lower than mean is 11. So we can say that data is distributed around mean
d) Null hypthesis is accepted
Test statistic= (sample mean-expected mean)/standard deviation
=(172.52-170)/10.31
= 0.024
P(Z> 0.024)= (1-0.5080)= 0.492
p-value= 2× 0.492= 0.984
Using 5% or 0.05 significance level,
test statistic is greater than significance level so null hypothesis is accepted
