You lose your court case in The previous problem. You decide you don\'t believe

Question

You lose your court case in The previous problem. You decide you don't believe the radar guns .ire operating the way they are supposed. You read up on radar guns and find out that although their errors are normally distributed and the standard deviation of their error rarely deviates from what the manufacturer says, they are often entire batches that miscalibrated so the mean of their error is not zero. To Prove your point, you get 25 radar guns and measure the error in the recorded speed of a car driving exactly 60mph. You find the average error from the 25 radar guns is 1.4 mph. a) In this problem, are you testing a claim (or belief) or whether or not some change that occurred affected the population mean? Answer b) What is the name of the distribution the sample mean In this problem come from? Answer: c) How do you know it comes from this distribution? (justify your answer in part b) Answer: d) What is the standard deviation of the distribution the sample mean in this problem comes from? Answer: e) If the true mean for the radar gun errors was zero, what percentile would the observed sample mean be in? Answer:

Explanation / Answer

Here we are given that,

n = number of radar guns = 25

Xbar = average error = 1.4 mph

a) Yes here we test the population mean.

For testing population mean here we need sample mean, standard deviation and sample size.

From these three values we can test the population mean.

b) The distribution of sample mean is normal with mean is mu and standard deviation is sd / sqrt(n).

where sd is standard deviation of the data.

c) Assumption for the distribution of sample mean are :

The Central Limit Theorem (CLT) The mean of a random sample has a sampling distribution whose shape can be approximated by a Normal model. The larger the sample, the better the approximation will be.

Assumptions: Independence Assumption

Sample Size Assumption

Conditions you can check:

Randomization Condition : The values must be sampled randomly.

10% Condition : If sampling is not with replacement, the sample size, n, must be no larger than 10% of the population.

Large Enough Sample Condition : If the population is unimodal and symmetric, any size sample is sufficient. Otherwise, a larger sample is needed

d) The standard deviation of the distribution the sample mean is :

sd = sd / sqrt(n)

where sd is standard deviation of the data.

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