Computer software generated 500 random numbers that should look like they are fr

Question

Computer software generated 500 random numbers that should look like they are from the uniform distribution on the interval 0 to 1 (see page 282). They are categorized into five groups: (1) less than or equal to 0.2,

(2) greater than 0.2 and less than or equal to 0.4,

(3) greater than 0.4 and less than or equal to 0.6,

(4) greater than 0.6 and less than or equal to 0.8, and

(5) greater than 0.8.

The counts in the five groups are 113, 95, 108, 99, and 85, respectively. The probabilities for these five intervals are all the same. What is this probability? Compute the expected number for each interval for a sample of 500. Finally, perform the goodness of fit test and summarize your results.
s.

Explanation / Answer

1)probabilities for these five intervals are =1/5 =0.2

2) expected number for each interval for a sample of 500 =500/5 =100

applying goodness of fit test:

for above test statistic 4.84 and (categories-1=5-1=4) degree of freedom ; p value =0.3041

as p value is high; we can not reject that above is a uniform distirbution

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E <=0.2 0.200 113.000 100.00 1.69 0.2-0.4 0.200 95.000 100.00 0.25 0.4-0.6 0.200 108.000 100.00 0.64 0.6-0.8 0.200 99.000 100.00 0.01 0.8-1.0 0.200 85.000 100.00 2.25 1 500 500 4.8400

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.