The shape, mean, and standard deviation of the sampling distribution of the difference in the two sample proportions is Shape = skewed right, mean = 0.35, standard deviation = 0.05.
What is the standard deviation?
In statistics, the standard deviation of a random variable, data is the square root of its variance.
An electronic prize wheel is programmed to land on "win” 25% of the time on weekdays and 10% of the time on weekends, and consecutive plays produce winners independently.
A random sample of 50 outcomes from this machine on a weekday and 100 outcomes from this machine on a weekend.
[tex]P_{1} = 25%\\ =0.25\\P_{2} = 0.10\\[/tex]
[tex]n_{1} = 50\\n_{2} =100[/tex]
Let x be a random variable for weekdays
[tex]x= N[0.25, 0.25\times(1-0.25)/50]\\x = N[0.25, 0.00375][/tex]
Let y be randomly variable for weekdays
[tex]Y= N[0.10, 0.10\times(1-0.10)/100]\\Y= N[0.10, 0.0009][/tex]
Thus, the shape, mean, and standard deviation of the sampling distribution of the difference in the two sample proportions is Shape = skewed right, mean = 0.35, standard deviation = 0.05.
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