A researcher investigated the number of days patients spend at a hospital. Patie
ID: 3232897 • Letter: A
Question
A researcher investigated the number of days patients spend at a hospital. Patients were randomly selected from four regions and the number of days each patient spent at a hospital was recorded. The accompanying table shows the results. At alpha = 0.10, can the researcher reject the claim that the mean number of day patients spend in the hospital is the same for all four regions? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Click the icon to view the counts for the number of days patients spent at a hospital. (a) Identify the claim and state H_0 and H_a. Choose the correct answer below. H_0: mu_1 = mu_2 = mu_3 = mu_4 (claim) H_a: At least one mean is different from the others. H_0: mu_1 = mu_2 = mu_3 = mu_4 = mu_5 = mu_6 H_a: At least one mean is different from the others. (claim) (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and The degrees of freedom for the numerator, d.f.N, is, and the degrees of freedom for the denominator, d.f_D, isExplanation / Answer
Solution
Part (a)
ANSWER Option A
Part (b) – All details are available in the ANOVA Table given below.
Degrees of freedom for the numerator = 3
Degrees of freedom for the denominator = 17
Critical value (given = 0.1) = F3, 17, 0.1 = 2.437
Value of F-statistic = 0.383
p-value = P(F3, 17 > ) = 0.7669
Significance: Since p-value > 0.1,(or Value of F-statistic < Fcrit), the test is not significant,
Decision: Since p-value > 0.1,(or Value of F-statistic < Fcrit), H0 is accepted.
Conclusion: There is enough statistical evidence to validate the researcher’s claim.
ANOVA
Source
DF
SS
MS
F
Fcrit
p-value
Region
3
5.119
1.706349
0.382522
2.437434
0.7669
Error
17
75.833
4.460784
Total
20
80.952
4.047619
DONE
ANOVA
Source
DF
SS
MS
F
Fcrit
p-value
Region
3
5.119
1.706349
0.382522
2.437434
0.7669
Error
17
75.833
4.460784
Total
20
80.952
4.047619
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