The data table contains waiting times of customers at a​ bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than
1.6
​minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of
0.025.
Assume that the sample is a simple random sample selected from a normally distributed population. Complete parts​ (a) through​ (d) below.
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Part 1
a. Identify the null and alternative hypotheses. Choose the correct answer below.
A.
H0: σ≥1.6
minutes
HA: σ<1.6
minutes
B.
H0: σ=1.6
minutes
HA: σ<1.6
minutesYour answer is correct.
C.
H0: σ<1.6
minutes
HA: σ=1.6
minutes
D.
H0: σ=1.6
minutes
HA: σ≠1.6
minutes
Part 2
b. Compute the test statistic.
χ2=enter your response here
​(Round to two decimal places as​ needed.)
6.3
6.3
7.2
7.2
7.3
7.4
7.5
7.2
6.7
6.2
6.1
7.7
6.4
7.8
6.5
7.1
7.2
6.8
7.9
8.8
6.7
7.8
7.1
8.9
7.8
7.2
6.5
6.1
6.9
6.8
5.6
7.2
8.4
7.8
6.2
7.8
7.2
6.3
7.2
6.2
7.2
8.3
7.8
6.4
6.3
6.9
6.4
7.2
7.8
7.9
8.9
7.6
6.9
8.3
7.4
8.5
6.9
7.4
6.5
7.9