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Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of 56 students were asked on which night of the week they did the most homework.
From the population of students, do the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week? Sunday Monday Wednesday Tuesday 107 Thursday 10 Friday 5 Saturday 5 Number of Students
a. Find the expected values
b. What is the df and critical value for the study with an alpha level of .05?
c. State the two hypotheses
d. Perform a chi square goodness of fit test
e. Report the results in sentence and numbers in APA format.

Sagot :

Akiran007idn

Answer:

a. Therefore the expected values are 8,8,8,8,8,8,8

b. The df = n-1= 7-1= 6

The critical value at ∝=  0.05  with 6 d.f is χ²≥χ²(d.f) 0.05= 12.59

c. The null hypothesis is the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week

against the claim the nights for the highest number of students doing the majority of their homework do not occur with equal frequencies during a week.

d.  χ² = 4.25

e.Results :  accept the null hypothesis

ei = 8,8,8,8,8,8,8

df =  6

H0:  σ²1 ≤ σ²2 against the claim  Ha: σ²1> σ²2

The critical region is  χ²≥χ²(0.05) 6= 12.59

The calculated value of χ² = 4.25 < χ²(0.05) 6= 12.59 therefor accept the null hypothesis.

Step-by-step explanation:

                                Sunday     Monday     Tuesday  Wednesday  

No of Students        11                  8              10                      7

                                Thursday       Friday       Saturday

                                   10                  5                5

a. The expected values are = Total number /no of days = 56/7= 8

Therefore the expected values are 8,8,8,8,8,8,8

b. The df = n-1= 7-1= 6

The critical value at ∝=  0.05  with 6 d.f is χ²≥χ²(d.f) 0.05= 12.59

c. The null hypothesis is the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week

against the claim the nights for the highest number of students doing the majority of their homework do not occur with equal frequencies during a week

H0:  σ²1 ≤ σ²2 against the claim  Ha: σ²1> σ²2 as the goodness of fit test is always right tailed

d.

Days   No.of Students

                Observed        Expected       oi-ei         (oi-ei)²           (oi-ei)²/ei

Sunday     11                     8                       3                9                   1.125

Monday    8                    8                          0                0                  0

Tuesday       10                   8                       2               4                  0.5

Wednesday     7                 8                       -1               1                   0.125

Thursday          10                 8                    2                2                  0.25

Friday               5                 8                     -3               9                   1.125

Saturday            5                 8                    -3               9                   1.125  

 ∑                                                                                                      4.25

e. since the calculated value of χ² = 4.25 is less than the critical value of

χ²= 12.59  we fail to reject H0 and conclude that the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week.

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