Question

Consider the observed frequency distribution for a set of grouped random variables available below. Perform a chi-square test using a α=0.10 to determine if the observed frequencies follow the normal probability distribution with μ=99 and σ=20.

Click the icon to view the observed frequency distribution.

Random Variable, x	Frequency, fo
Less than 79	10
79 to under 99	14
99 to under 119	18
119 and more	8
Total	50

State the appropriate null and alternative hypotheses. What is the null hypothesis?

A.H 0 : The mean number of the random variable is not equal to 99.

B.H 0 : The random variable follows the normal probability distribution.

C.H 0 : The mean number of the random variable is equal to 99.

D.H 0 : The random variable does not follow the normal probability distribution.

What is the alternative hypothesis?

A.H 1 : The mean number of the random variable is equal to 99.

B.H 1 : The random variable does not follow the normal probability distribution.

C.H 1: The mean number of the random variable is not equal to 99.

D.H 1 : The random variable follows the normal probability distribution.

Calculate the chi-square test statistic,

X2=

(Round to two decimal places as needed.)

Determine the p-value.

p-value=

(Round to three decimal places as needed.)

State the appropriate conclusion. ▼ Reject OR Do not reject H 0. There is ▼ insufficient OR sufficient evidence to conclude that the random variable does not follow the normal probability distribution.

Answer 1

null hypothesis: Ho:

observed frequencies follow the normal probability distribution with mu= 99 and sigma=20

alternate hypothesis:Ha: observed frequencies does not follow the normal probability distribution with mu= 99 and sigma=20

Chi square Test statistic = 1.141487239

p-value =0.5811

for p value is very high; Do not reject  H 0. There is insufficient evidence to conclude that the random variable does not follow the normal probability distribution.