Question

A police department released the numbers of calls for the different days of the week during the month of​ October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis?

Day Sun Mon Tues Wed Thurs Fri Sat

Frequency 153 210  224 248 174 212 231

Determine the null and alternative hypotheses.

Upper H 0​: (1)

Upper H 1​:

(2) Calculate the test​ statistic ​(Round to three decimal places as​ needed.)

(3) Calculate the​ P-value ​(Round to four decimal places as​ needed.)

(4) What is the conclusion for this hypothesis​ test?

A. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

B. Fail to reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls

C. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

D. Reject Upper H 0. There is insufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

(5) What is the fundamental error with this​ analysis?

A. Because October has 31​ days, two of the days of the week occur more often than the other days of the week.

B. Because October has 31​ days, one of the days of the week occur more often than the other days of the week.

C. Because October has 31​ days, each day of the week occurs the same number of times as the other days of the week.

D. Because October has 31​ days, three of the days of the week occur more often than the other days of the week.

(1) Police calls occur with the same frequency on the different days of the week.

At least one day has a different frequency of calls than the other days.

Police calls occur with all different frequencies on the different days of the week.

At least two days have a different frequency of calls than the other days.

(2) Police calls occur with all different frequencies on the different days of the week.

At least one day has a different frequency of calls than the other days.

Police calls occur with the same frequency on the different days of the week.

At least two days have a different frequency of calls than the other days.

Answer 1

Upper H 0​: (1) Police calls occur with the same frequency on the different days of the week.

H 1​: At least one day has a different frequency of calls than the other days.

2)

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	1/7	153	207.43	-3.78	14.282
2	1/7	210	207.43	0.18	0.032
3	1/7	224	207.43	1.15	1.324
4	1/7	248	207.43	2.82	7.935
5	1/7	174	207.43	-2.32	5.387
6	1/7	212	207.43	0.32	0.101
7	1/7	231	207.43	1.64	2.679
total	1.000	1452	1452		31.7397
test statistic X2 =		31.740

3)

p value =

0.0000

A. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

D. Because October has 31​ days, three of the days of the week occur more often than the other days of the week.