Question

McDonalds claims that it can deliver the order within 40 minutes. From the data of 65 randomly selected deliveries it was found that the average delivery time was 50 minutes with a standard deviation of 10 minutes.                                                                   

1. State the null and alternate hypotheses
2. Calculate the test statistic
3. Validate the claim at 0.01 level of significance

Answer 1

a) Null hypothesis : The Mean time to deliver the order () is greater than 40 minutes.

i.e,

Alternative hypothesis : Mean time to deliver the order is within 40 minutes.

i.e,

b) Test statistic is given by -

is the sample mean time to deliver the order = 50 min

is the specified value of population average time to deliver the order under the null hypothesis = 40 min

s is the sample standard deviation = 10 min

n is the sample size = 65

So, the value of the test statistic will be -

  

= 8.064

c) Degrees of freedom = n - 1 = 64

The critical value of t with 64 degrees of freedom for one tailed test at 0.01 level of significance is nearly equal to the critical value of z at 0.01 level of significance for one tailed test (since, sample size is large) = 2.3

[It can be obtained from the z table by finding the z corresponding to the area nearly equal to 0.01]

Now, the calculated t > critical value of t, hence, we may reject the null hypothesis at 0.01 level of significance, hence, we conclude that mean time to deliver the order is wuthiw 40 minutes.

Hence, the claim of McDonald's was true.