Assignment:
Indicate the statistical test, the degrees of freedom, the level of significance, the region of rejection, the critical value, the calculated value of the test statistic, and the probability.
Situation A
The number of new US book titles increased from almost 47,000 in 1990 to over 48,000 in 1991. However, this was still below the historic high of about 56,000 titles attained in 1987 (Grannis, 1992). Can we expect an increase or decrease in price of books, especially hardbacks, if there are more competitors in the market? The following table gives the number of titles and the average price of hardback books classified according to 23 standard subject categories representing one or more specific Dewey Decimal Classification numbers.
Table
Book Subject Categories Based on Dewey Decimal Classification
1990 1991
Category Volume Average Price ($) Volume Average Price ($)
Agriculture 359 52.24 371 57.73
Art 759 42.18 717 44.99
Biography 1337 28.58 1416 27.52
Business 748 45.48 790 43.38
Education 562 38.72 556 41.26
Fiction 1962 19.83 2062 21.30
General Works 1035 54.77 1071 51.74
History 1450 36.43 1442 39.87
Home Economics 357 23.80 341 24.23
Juveniles 3675 13.01 3705 16.64
Language 312 42.98 240 51.71
Law 596 60.78 240 63.89
Literature 1312 35.80 1265 35.76
Medicine 2215 72.24 2078 71.44
Music 184 41.86 173 41.04
Philosophy/Psychology 963 40.58 945 42.74
Poetry/Drama 486 32.19 511 33.29
Religion 977 31.31 958 32.33
Science 2028 74.39 958 80.14
Sociology/Economics 4504 42.10 4306 48.83
Sports/Recreation 403 30.52 440 30.68
Technology 1521 76.48 1620 76.40
Travel 181 30.41 156 33.50
Consider the number of volumes and average price per volume in 1990 and in 1991 as paired samples for two randomly selected years of 23 categories of books.
1. Determine whether the difference in the average number of volumes per category for 1991 differs significantly from the 1990 average.
2. Determine whether the change in the average price of a hardback book per category in 1991 differs significantly from that in the 1990 average.
3. Summarize your results concerning the difference in the number and price of books per category in 1991 compared with 1990.
Do the data provide sufficient evidence to indicate volume and price variability between 1990 and 1991? Also indicate whether the null hypothesis is rejected or not rejected, the type of error possibly made, and the conclusion or answer to the stated research question. Use the 8-step of hypothesis testing procedure to report the findings