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

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