The mean waiting time at the drive-through of a fast-food restaurant from the ti

Question

The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.3 seconds. A manager devised a new drive-through system at his restaurant and measured the wait time for 10 randomly selected orders:

108.5      67.5      58.0      74.9      65.1      80.4      95.5      86.3     70.9      72.0

(Sample mean = 77.91             Sample standard deviation = 15.216)

Assume the data are normally distributed with no outliers. The manager believes the new times are shorter than before.

(a) State the claim and the alternate hypothesis.

(b) What type of test used to evaluate the manager’s claim?

(c) What is the p-value?

(d) With a significance level of 0.05, do you reject the null hypothesis or not reject the null hypothesis?

Explanation / Answer

a) null hypothesis: mean =84.3

claim and alternate hypothesis:mean<84.3

b) we wil use one sample t test

c) std error=std deviation/(n)1/2 =4.8117

hence test stat t=(X-mean)/std error =(77.91-84.3)/4.8117=-1.328

for above test stat p value =0.1084

d)as p vlaue is greater then 0.05 level ; we can not reject null hypothesis

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