Question
At a shooting range, instructors can determine if a shooter is consistently missing the target because of the gun sight or because of the shooter’s
ability. If a gun’s sight is off, the variance of the distances between the shots and the center of the shot pattern will be small (even if the shots are not
in the center of the target). A student claims that it is the sight that is off, not his aim, and wants the instructor to confirm his claim. If a skilled shooter
fires a gun at a target multiple times, the distances between the shots and the center of the shot pattern, measured in centimeters (cm), will have a
variance of less than 0.33 . After the student shoots 30 shots at the target, the instructor calculates that the distances between his shots and the
center of the shot pattern, measured in cm, have a variance of 0.21 . Does this evidence support the student’s claim that the gun’s sight is off? Use a
0.10 level of significance. Assume that the distances between the shots and the center of the shot pattern are normally distributed.
Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
ability. If a gun’s sight is off, the variance of the distances between the shots and the center of the shot pattern will be small (even if the shots are not
in the center of the target). A student claims that it is the sight that is off, not his aim, and wants the instructor to confirm his claim. If a skilled shooter
fires a gun at a target multiple times, the distances between the shots and the center of the shot pattern, measured in centimeters (cm), will have a
variance of less than 0.33 . After the student shoots 30 shots at the target, the instructor calculates that the distances between his shots and the
center of the shot pattern, measured in cm, have a variance of 0.21 . Does this evidence support the student’s claim that the gun’s sight is off? Use a
0.10 level of significance. Assume that the distances between the shots and the center of the shot pattern are normally distributed.
Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
Ask by Hampton Kelly. in the United States
Nov 16,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of the test statistic is approximately 18.455.
Solution

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Mind Expander
To compute the test statistic for the variance, we can use the chi-square (
) test formula. The formula for the test statistic is:
where:
-
is the number of samples -
is the sample variance -
is the population variance under the null hypothesis
In this case:
Substituting the values:
Calculating it step by step:
Rounding to three decimal places, the value of the test statistic is:
So the computed value of the test statistic is 18.455.