Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches. A baseball analyst wonders whether the standard deviation of heights of major- league baseball players is less than 2.5 inches. The heights( in inches) of 20 randomly selected players are shown in the table. Test the notion at the a=0.05 level of significance What are the correct hypothesis for this test? The null hypothesis is Ho: __ __ 2.5 The alternative hypothesis is H1: __ __ 2.5 Calculate the value of the test statistic x2=_____(Round to 3 decimal places as needed) Use the technology to determine the P-value for the test statistic The P-value is ___(Round to 3 decimal places as needed) What's the correct conclusion at the a=0.05 level of significance? Since the P-value is ____ than the level of significance. ____ the null hypothesis. There___ sufficient evidence to conclude that the standard deviation of heights of major-league baseball players is less than 2.5 inches at the 0.05 level of significance.
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!
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches. A baseball analyst wonders whether the standard deviation of heights of major- league baseball players is less than 2.5 inches. The heights( in inches) of 20 randomly selected players are shown in the table.
Test the notion at the a=0.05 level of significance
What are the correct hypothesis for this test?
The null hypothesis is Ho: __ __ 2.5
The alternative hypothesis is H1: __ __ 2.5
Calculate the value of the test statistic
x2=_____(Round to 3 decimal places as needed)
Use the technology to determine the P-value for the test statistic
The P-value is ___(Round to 3 decimal places as needed)
What's the correct conclusion at the a=0.05 level of significance?
Since the P-value is ____ than the level of significance. ____ the null hypothesis. There___ sufficient evidence to conclude that the standard deviation of heights of major-league baseball players is less than 2.5 inches at the 0.05 level of significance.
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