Question

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.

a. .0500 b. .0228 c. .0456 d. .0250

Answer 1

The correct option is B) 0.0228

Explanation:

Consider the provided information.

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute.

Thus, the value of n = 100,
`\bar x=3.1` and σ = 0.5

We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.

The null and alternative hypotheses are,

`H_0:\mu\leq3` and
`H_a:\mu>3`

Compute the test statistic
`z=(\bar x-\mu)/((\sigma)/(√(n)))`

`z=(3.1-3)/((0.5)/(√(100)))`

`z=(0.1)/(0.05)`

`z=2`

By using the table.

P value = P(Z>2) = 0.0228

Hence, the correct option is B) 0.0228