In Major League baseball, do Left-Handed hitters and Right-Handed hitters tend to have different batting averages? We will study this question by taki

Cheyanne Leigh 2021-05-17 Answered

In Major League baseball, do Left-Handed hitters and Right-Handed hitters tend to have different batting averages? We will study this question by taking random samples of m=45 seasonal batting averages from left-handed batters and n=53 seasonal batting averages from right-handed batters. The mean batting averages were x= .256 for the left-handers and y=.254 for the right-handers. It is recognized that the true standard deviations of batting averages are \(\sigma\);x = .0324 for left-handed batters and \(\sigma\);y = .0298 for right-handed batters. The true (unknown) mean batting average for left-handers = \(\mu\)x , while the true unknown mean batting average for right-handers = \(\mu\)y . We would like to examine \(\mu x- \mu y \) . a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x - y ? c) Create a 98% confidence interval for \(\mu x- \mu y \)? d) What is the length of the confidence interval in part c) ?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Delorenzoz
Answered 2021-05-18 Author has 22586 answers
a) 0.0324
b) 0.0063
c) -0.0128,0.0168
d) 0.0296
Not exactly what you’re looking for?
Ask My Question
11
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a \(99\%\) confidence interval for the proportion of adult residents who are parents in a given county.
Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places \(\displaystyle<{p}<\) Express the same answer using a point estimate and a margin of error. Give your answers as decimals, to three places.
\(\displaystyle{p}=\pm\)

asked 2021-08-10

A local firm manufactures LED products that have a lifespan that is approximately normally distributed with a std. dev. of 30 hours. If a sample of 30 LED products has an average lifespan of 780 hours, find a \(\displaystyle{96}\%\) confidence interval for the population mean of all LED products produced by this firm.
Choose 2 answers in nearest unit (ones) or in whole number.
Example, if your answer is \(\displaystyle{888.83}\leq\mu\leq{899.56}\), choose 889 and 900.
\(\begin{array}{|c|c|}\hline 775 & 773 & 807 & 797 & 791 & 769 & 789 & 768 & 805 & 763 & 771 & 792 \\ \hline \end{array}\)

asked 2021-05-25

Suppose we have two independent random variables x1 and x2 with respective population means \(\mu\);1 and \(\mu\);2. Let us say that we use sample data to construct two 80% confidence intervals. Confidence Interval amp; Confidence Level A1 lt \(\mu\) 1 lt;B1 amp;0.80 ​
A2 lt \(\mu\)2 lt;B2 amp;0.80
Now, what is the probability that both intervals hold at the same time? Use methods to show that
P(A1<\(\mu\);1)

asked 2021-05-05
What is meant by the term “90% confident” when constructing a confidence interval for a mean? a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval. b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean. c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
asked 2021-08-02

A study a local high school tried to determine the mean height of females in the US. A study surveyed a random sample of 125 females and found a mean height of 64.5 inches with a standard deviation of 5 inches. Determine a \(\displaystyle{95}\%\) confidence interval for the mean.
\(\begin{array}{|c|c|} \hline \text{Confidence Interval} & z \\ \hline 80\% & 1.282 \\ \hline 85\% & 1.440\\ \hline 90\% & 1.645\\ \hline 95\% & 1.960\\ \hline 99\% & 2.576\\ \hline 99.5\% & 2.807\\ \hline 99.9\% & 3.291\\ \hline \end{array}\)

asked 2021-06-07

Consider a normal population distribution with the value of \(\sigma\) known?
c.What value of \(\displaystyle{\frac{{\alpha}}{{{2}}}}\) in the CI formula (7.5)results in a confidence level of 99.7%?
d. Answer the question posed in part (c) for a confidence level of 75%?

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question
...