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In a survey, 30 random customers who purchased concessions at a movie theater listed the money they spent. The standard deviation was found to be $1.28. Find the critical value(s) needed to test a claim that the standard deviation of all individual money spent at the concession stand at movie theaters is equal to $1.45. Use a 0.05 significance level.
a. 16.047
b. 17.708, 42.557
c. 17.708
d. 16.047, 45.722

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Work Shown:

= sigma = population standard deviation

The hypotheses are

We have a two tailed test as indicated by the alternative hypothesis. So there will be 2 chi-square critical values.

We want to find values of A and B such that

note how is the confidence level.

The two tails combine to form alpha = 0.05, so half of that is alpha/2 = 0.05/2 = 0.025

Each tail has an area of 0.025

The chi-square distribution is NOT symmetric, so we cannot use tricks earlier done with the normal distribution.

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Use a chi-square table to find the area to the right of 45.722 is roughly 0.025, so , therefore B = 45.722 approximately.

The degrees of freedom are df = n-1 = 30-1 = 29.

With the same degrees of freedom, use the table to find that which shows that A = 16.047 approximately.

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updates to

The two critical values are 16.047 and 45.722

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: