Baseball has always been a favorite pastime in America and is rife with statistics and theories. In a paper, researchers showed that major league players who have nicknames live an average of 2½ years longer than those without them (The Wall Street Journal, July 16, 2009). You do not believe in this result and decide to collect data on the lifespan of 30 baseball players along with a nickname variable that equals 1 if the player had a nickname and 0 otherwise. The data are shown in the accompanying table and are contained in the accompanying Excel file. (You may find it useful to reference the appropriate table: z table or t table) Years Nickname Years Nickname Years Nickname 74 1 61 0 68 1 62 1 64 0 68 0 67 1 70 0 64 1 73 1 71 1 67 1 49 1 69 1 64 0 62 0 56 0 63 1 56 0 68 1 68 1 63 0 70 1 68 1 80 1 79 1 74 0 65 1 67 0 64 0 Click here for the Excel Data File Let Samples 1 and 2 represent major-league players with and without nicknames, respectively. a. Create two subsamples consisting of players with and without nicknames. Calculate the average longevity for each subsample. (Round your answers to 4 decimal places.) b. Specify the hypotheses to contradict the claim made by researchers. multiple choice 1 H0: μ1 − μ2 = 2.5; HA: μ1 − μ2 ≠ 2.5 H0: μ1 − μ2 ≥ 2.5; HA: μ1 − μ2 < 2.5 Incorrect H0: μ1 − μ2 ≤ 2.5; HA: μ1 − μ2 > 2.5 c-1. Calculate the value of the test statistic. Assume that the population variances are unknown but equal. (Round your answer to 3 decimal places.) c-2. Find the p-value. multiple choice 2 p-value ≤ 0.01 0.01 < p-value ≤ 0.02 0.02 < p-value ≤ 0.05 0.05 < p-value ≤ 0.10 p-value > 0.10 Correct d. What is the conclusion of the test using a 5% level of significance? multiple choice 3 Reject H0; the sample data disproves the claim by the researchers. Reject H0; the sample data does not disprove the claim by the researchers. Incorrect Do not reject H0; the sample data disproves the claim by the researchers. Do not reject H0; the sample data does not disprove the claim by the researchers.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Baseball has always been a favorite pastime in America and is rife with statistics and theories. In a paper, researchers showed that major league players who have nicknames live an average of 2½ years longer than those without them (The Wall Street Journal, July 16, 2009). You do not believe in this result and decide to collect data on the lifespan of 30 baseball players along with a nickname variable that equals 1 if the player had a nickname and 0 otherwise. The data are shown in the accompanying table and are contained in the accompanying Excel file. (You may find it useful to reference the appropriate table: z table or t table)
| Years | Nickname | Years | Nickname | Years | Nickname | |||
| 74 | 1 | 61 | 0 | 68 | 1 | |||
| 62 | 1 | 64 | 0 | 68 | 0 | |||
| 67 | 1 | 70 | 0 | 64 | 1 | |||
| 73 | 1 | 71 | 1 | 67 | 1 | |||
| 49 | 1 | 69 | 1 | 64 | 0 | |||
| 62 | 0 | 56 | 0 | 63 | 1 | |||
| 56 | 0 | 68 | 1 | 68 | 1 | |||
| 63 | 0 | 70 | 1 | 68 | 1 | |||
| 80 | 1 | 79 | 1 | 74 | 0 | |||
| 65 | 1 | 67 | 0 | 64 | 0 | |||
Click here for the Excel Data File
Let Samples 1 and 2 represent major-league players with and without nicknames, respectively.
a. Create two subsamples consisting of players with and without nicknames. Calculate the average longevity for each subsample. (Round your answers to 4 decimal places.)
b. Specify the hypotheses to contradict the claim made by researchers.
multiple choice 1
-
H0: μ1 − μ2 = 2.5; HA: μ1 − μ2 ≠ 2.5
-
H0: μ1 − μ2 ≥ 2.5; HA: μ1 − μ2 < 2.5 Incorrect
-
H0: μ1 − μ2 ≤ 2.5; HA: μ1 − μ2 > 2.5
c-1. Calculate the value of the test statistic. Assume that the population variances are unknown but equal. (Round your answer to 3 decimal places.)
c-2. Find the p-value.
multiple choice 2
-
p-value ≤ 0.01
-
0.01 < p-value ≤ 0.02
-
0.02 < p-value ≤ 0.05
-
0.05 < p-value ≤ 0.10
-
p-value > 0.10 Correct
d. What is the conclusion of the test using a 5% level of significance?
multiple choice 3
-
Reject H0; the sample data disproves the claim by the researchers.
-
Reject H0; the sample data does not disprove the claim by the researchers. Incorrect
-
Do not reject H0; the sample data disproves the claim by the researchers.
-
Do not reject H0; the sample data does not disprove the claim by the researchers.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
