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Null & Alternative Hypotheses: Retail Prices

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The R.R. Bowker Company of New York collects information on the retail prices of collectible children's books and publishes its findings in Publisher's Weekly. Last year, the mean retail of collectible children's books was $35.44. A random sample of 40 collectible children's books (published this year) is selected, the retail prices are noted, and the results are as follows:

Sample Size: 40
Sample Mean: $38.75
Sample Standard Deviation: $7.35

Does the sample data provide evidence to conclude that the mean retail price of collectible children's books has increased over last year (using a= .10)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e, What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does this sample data provide evidence (with a=0.10), that the mean retail price of collectable children's books has increased over last year?

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The null hypothesis tested is
H0: Mean retail price of collectible children's ...

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Null & Alternative Hypotheses: Retail Prices

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Hypothesis Testing Problems,

Example 1: Suppose data on retail prices of a cholesterol reducing drug were collected from randomly selected Pharmacies of two states (16 pharmacies from State1 and 13 from State 2) with the following values:
State 1 State2
125.05 145.32
137.56 131.19
142.5 151.65
145.95 141.55
117.49 125.99
142.75 126.29
121.99 139.19
117.49 156
141.64 137.56
128.69 154.1
130.29 126.41
142.39 114
121.99 144.99
Given the two samples can we conclude that the average retail prices do not significantly differ by State? Give conclusion for two cases (a) population variances are equal; and (b) population variances are unequal.
Solve this problem using calculator, with formulas and the t-table. Work with t-values only.

Example 2: A study was conducted to determine if there was a difference in humor content in British and American trade magazine advertisements. An independent random sample of 203 British trade magazines contained 54 humorous ads while the other independent sample of 270 American trade magazine advertisements contained 56 humors. Does this data set provide evidence that there are more frequent humorous content in ads of British compared to American trade magazines?
Work it out with calculator, Z table and the formulas.

Example 3: A recent national survey of hospital admissions for people between 25 and 50 years who had hospital admissions in during a two years' period showed that 30% had 1 admission only, 25% had two admissions, 15% had 3 admissions, 12% had 4 admissions, 8 % had 5 admissions, 10% had 6 admissions or more admissions. The mayor of a small city claims that his city is much healthier than the national average. He even cites the percentages for the two extreme categories. He says that 40% of local population in the given age group have only one hospital admissions (compared to 30% national) and the percentage of 6 or more admissions is only 5% compared to national 10%. His claim was in fact based on a sample of 300 randomly selected people in the specified age group who were interviewed by a local Newspaper. It was revealed that 120 people had only 1 admission, 81 had 2 admissions, 48 had 3 admissions, 18 had 4 admissions, 18 had 5 admissions, and 15 had 6 admissions or more admissions. Does the data support the mayor's claim? Please use Excel for calculation.

Example 4: Test H0: ?1 ? ?2; H1: ?1 > ?2 at ? = .05, when X ?1 = 75.4, X ?2 = 72.2, s1 = 3.3, s2 = 2.1, n1 = 6, n2 = 6. Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed. Please use Excel for calculation.

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