Question

Are phone calls equally likely to occur any day of the week? The day of the week for each of 504 randomly selected phone calls was observed. The results are displayed in the table below. Use an αα = 0.05 significance level.

1. Complete the rest of the table by filling in the expected frequencies:

   Frequencies of Phone Calls for Each Day of the Week

   Outcome	Frequency	Expected Frequency
   Sunday	56
   Monday	52
   Tuesday	61
   Wednesday	92
   Thursday	73
   Friday	92
   Saturday	78

2. What is the correct statistical test to use? Select an answer (Goodness-of-Fit, Homogeneity, Independence, Paired t-test)
3. What are the null and alternative hypotheses?
   H0:
   • Phone calls and days of the week are independent.
   • The distribution of phone calls is uniform over the days of the week.
   • The distribution of phone calls is not uniform over the days of the week.
   • Phone calls and days of the week are dependent.
4. H1:
   • The distribution of phone calls is uniform over the days of the week.
   • The distribution of phone calls is not uniform over the days of the week.
   • Phone calls and days of the week are dependent.
   • Phone calls and days of the week are independent.
5. The degrees of freedom = _____
6. The test-statistic for this data = ____ (Please show your answer to three decimal places.)
7. The p-value for this sample = _____ (Please show your answer to four decimal places.)
8. The p-value is (greater than, less than or equal to) α
9. Based on this, we should? (reject the null, fail to reject the null, accept the null)
10. Thus, the final conclusion is...
    • There is insufficient evidence to conclude that phone calls and days of the week are dependent.
    • There is sufficient evidence to conclude that the distribution of phone calls is not uniform over the days of the week.
    • There is insufficient evidence to conclude that the distribution of phone calls is not uniform over the days of the week.
    • There is sufficient evidence to conclude that the distribution of phone calls is uniform over the days of the week.
    • There is sufficient evidence to conclude that phone calls and days of the week are dependent.

Answer 1

1).the completed table be:-

days	observed	expected
sunday	56	504/7 = 72
monday	52	72
tuesday	61	72
wednesday	92	72
thursday	73	72
friday	92	72
saturday	78	72
	sum = 504

2).the correct statistical test to use : Goodness-of-Fit

3). H₀ : The distribution of phone calls is uniform over the days of the week.

4). H₁ : The distribution of phone calls is not uniform over the days of the week.

5).The degrees of freedom = (7-1) = 6

6). The test-statistic for this data :-

x =Σ (obs - erp) Erp (56 – 72)? 72 + + (78 - 72)? 72 & 22.417

7).The p-value for this sample = 0.0010

[ in any blank cell of excel type =CHISQ.DIST.RT(22.417,6) ]

8).The p-value is : less than or equal to $\alpha$

[ p value = 0.0010 <0.05 ]

9).Based on this, we should:  reject the null

10). conclusion:-

There is sufficient evidence to conclude that the distribution of phone calls is not uniform over the days of the week.

*** if you have any doubts about the problem please mention it in the comment box... if satisfied please LIKE.