A researcher investigated the number of days patients spend at a hospital. Patie

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 =0.10, can the researcher reject the claim that the mean number of days 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 Ho and Ha. Choose the correct answer below H At least one mean is different from the others. (claim) H: At least one mean is different from the others 0 D. Ho: At least one mean is different from the others. (claim) H: 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 determine the rejection regiorn. The degrees of freedom for the numerator, d.f.N isand the degrees of freedom for the denominator, d.f.p. is The critical value is F The rejection region i5 F (Round to two decimal places as needed.) (c) Calculate the test statistic. Round to three decimal places as needed.)

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

Hypotheses: Option B is correct.

b) d.f.N = 3

d.f.D = 17

Critical value = 2.44

Rejection Region is F > 2.44

c) Test statistic = 0.661

d) Option C is correct.

Interpretation of decision: is not; reject; same for all four regions.

Column n Mean Std. Dev. Std. Error North 6 5.6666667 2.7325202 1.1155467 East 6 4.3333333 1.3662601 0.55777335 South 4 4.25 1.5 0.75 West 5 4.8 1.3038405 0.58309519

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