Question

Consider the following discrete probability distribution along with observed frequencies for each day of the week. Complete parts a and b below.

Weekday Monday Tuesday Wednesday Thursday Friday Total

Probability 0.10 0.20 0.05 0.30 0.35 1.00

Observed​ Frequency, f Subscript o 12 26 9 39 44 130

a. Perform a​ chi-square test using alphaequals0.05 to determine if the observed frequencies follow a discrete probability distribution. Determine the null and alternative hypotheses. Choose the correct answer below.

A. Upper H 0​: The distribution of the variable differs from the normal distribution. Upper H 1​: The distribution of the variable is the normal distribution.

B. Upper H 0​: The distribution of the variable is the same as the given distribution. Upper H 1​: The distribution of the variable differs from the given distribution.

C. Upper H 0​: The expected frequencies are all equal to 5. Upper H 1​: At least one expected frequency differs from 5. D. Upper H 0​: The distribution of the variable differs from the given distribution. Upper H 1​: The distribution of the variable is the same as the given distribution.

Compute the value of the test​ statistic. ​(Round to two decimal places as​ needed.)

Identify the critical value. T​(Round to two decimal places as​ needed.)

Does the data provide sufficient evidence that the distribution of the variable differs from the given​ distribution?

A. Yes​, because there is sufficient evidence to reject the null hypothesis.

B. No​, because there is not sufficient evidence to reject the null hypothesis.

C. No​, because there is sufficient evidence to reject the null hypothesis.

D. Yes​, because there is not sufficient evidence to reject the null hypothesis.

b. Determine the​ p-value and interpret its meaning. ​p-valuee ​(Round to three decimal places as​ needed.)

Interpret the​ p-value. The​ p-value is the probability of observing a test statistic (greater than/ equal to/ less than) the part a​ statistic, assuming (the distribution of the variable differs from the given distribution/ at least one expected frequency differs from 5/ the expected frequencies are all equal to 5/ the distribution of the variable differs from the normal distribution/ the distribution of the variable is the normal distribution/ the distribution of the variable is the same as the given distribution)

Answer 1

a)

option B is correct

B. Upper H 0​: The distribution of the variable is the same as the given distribution. Upper H 1​: The distribution of the variable differs from the given distribution.

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.1000	12.0	13.00	-0.28	0.077
2	0.2000	26.0	26.00	0.00	0.000
3	0.0500	9.0	6.50	0.98	0.962
4	0.3000	39.0	39.00	0.00	0.000
5	0.3500	44.0	45.50	-0.22	0.049
total	1.000	130	130		1.0879
test statistic X2 =		1.09

for 0.05 level and 4 df :crtiical value X2 =

9.49

B. No​, because there is not sufficient evidence to reject the null hypothesis.

b)

p value =0.896

The​ p-value is the probability of observing a test statistic greater than the part a​ statistic, assuming the distribution of the variable is the same as the given distribution