Section 13.1: Categorical Data and the Multinomial Experiment Properties of the

Question

Section 13.1: Categorical Data and the Multinomial Experiment Properties of the Multinomial Experiment · The experiment consists of n identical trials. 2. There are k possible outcomes to each trial. These outcomes are sometimes called classes, 3. The probabilities of the k outcomes, denoted by 4.The trials are independent. categories or cells. PPP where P:+P.P, remain the same from trial to trial. , n of the number of observations The random variables of interest are the cell counts ni , n: that fall into each of the k categories. 5· Section 13.2:T esting Categorical Probabilities: One-Wav Table In this section we will consider a multinomial experiment with k outcomes that correspond to the categories of a single qualitative variable Conditions Required for a Valid ,- Test: One-Way Table 1.A multinomial experiment has been conducted. This is generally satisfied by taking a random 2. The sample size n will be large enough so that, for every cell, the expected cell count Em)will sample from the population of interest. be equal to 5 or more Test of Hypothesis about Multinomial Probabilities: One-Way Table H.: At least one p does not equal its hypothesized value where A,0, p.....,M,0 represent the hypothesized values of the multinomial probabilities Observed Expected] Expected where Enpo is the expected cell count- that is, the expected number of outcomes of type i, assuming that H1s true. The total sample size is n. R.R. We'll reject H, if r >

Explanation / Answer

Ans:

Expected freq.

E=pi*581

Test statistic:

Calculated chi square score=3.754

df=4-1=3

p-value=CHIDIST(3.754,3)=0.2893

As,p-value>0.05,we fail to reject null hypothesis.

There is insufficient evidence to conclude that there has been a chhange in the claimed distribution.

Response Observed freq. pi

Expected freq.

E=pi*581

(O-E)^2/E At home 389 0.7 406.7 0.770 At work 110 0.17 98.77 1.277 commuting 55 0.08 46.48 1.562 other 27 0.05 29.05 0.145 Total 581 1 581 3.754

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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