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 3.11 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. If the test statistic is 2.2, what is the p-value associated with this hypothesis test?(Round your answer to three decimal places.)

Answer 1

At 0.05 significance level, the p-value is 0.014

Explanation:

We are given the following in the question:

Population mean, μ = 3 minutes

Sample mean,
`\bar{x}` = 3.11 minutes

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, σ = 0.5 minutes

First, we design the null and the alternate hypothesis

`H_(0): \mu = 3\text{ minutes}\\H_A: \mu > 3\text{ minutes}`

We use one-tailed z test to perform this hypothesis.

Formula:

`z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

`z_(stat) = 2.2`

Now, we calculate the p-value from the normal standard z-table.

P-value = 0.014

At 0.05 significance level, the p-value is 0.014