Question

To test H0: σ=70 versus H1: σ<70​, a random sample of size n equals 25 is obtained from a population that is known to be normally distributed.

​(a) If the sample standard deviation is determined to be s equals = 46.5​, compute the test statistic.

​(b) If the researcher decides to test this hypothesis at α=0.05 level of​ significance, use technology to determine the​ P-value.

​(c) Will the researcher reject the null​ hypothesis?

What is the P-Value?

Answer 1

a)

Ho :   σ =   70
Ha :   σ <   70
      

sample Std dev ,    s =    46.5
Sample Size ,   n =    25
      
Chi-Square Statistic   X² = (n-1)s²/σ² = 24*46.5²/70² = 10.591(answer)

b)

degree of freedom,   DF=n-1 =    24
       

p-value   =   0.0084                                [excel function :     =chisq.dist(10.59,24,True) ]

c)

p value <α=0.05,    reject Ho

researcher will reject the null​ hypothesis