Question

In addition to concern about the amount of time cars spend in the drive-through, the manager is also worried about the variability in wait times. Prior to the new drive-through system, the standard deviation of wait times was 18.0 seconds. Use the data in the table below to decide whether there is evidence to suggest the standard deviation wait-time is less than 18.0 seconds. Use the α = 0.05 level of significance.

108.5	67.4	58.0	75.9	65.1
80.4	95.5	86.3	70.9	72.0

Conditions:
a) The χ² ("chi-square") test for standard deviations____ (is / is not) appropriate for this data.

Rejection Region:
b)To test the given hypotheses, we will use a____ (left / right / two) -tailed test.  
c) The appropriate critical value(s) for this test is/are_____ .  

d) The test statistic for this test is χ²₀=___.  report your answer rounded to 3 decimal places

e) We _____(reject / fail to reject) H₀.
f) The given data _____ (does / does not) provide significant evidence that the standard deviation of wait times under the new method is less than 18.0 seconds.

Answer 1

a) The χ2 ("chi-square") test for standard deviations____ (is ) appropriate for this data.

Rejection Region:
b)To test the given hypotheses, we will use a____ (left ) -tailed test.  
c) The appropriate critical value(s) for this test is/are_____ .  

d) The test statistic for this test is χ20=3.325.  report your answer rounded to 3 decimal places

e) We _____(fail to reject) H0.
f) The given data _____ (does not) provide significant evidence that the standard deviation of wait times under the new method is less than 18.0 seconds.

Null hypothesis	H₀: σ = 18
Alternative hypothesis	H₁: σ < 18

Method	Test Statistic	DF	P-Value
Bonett	—	—	0.310
Chi-Square	6.42	9	0.303