Question

There are 2 questions in this assignment. Your answers to each of these parts must be hand-written (preferably in pen) and include a diagram or diagrams and any calculations

2. In many bank branches across Canada, new ATM machines have been installed which no longer require users to place cheques and money in envelopes before inserting them into the machines. Did these new ATM machines affect how long customers spent depositing cheques and money? With the old ATM machines, it was determined that the true average amount of time spent depositing cheques and currency was 1.30 minutes. A random sample of 30 customers at a randomly selecting branch which had these new machines was observed depositing cheques and currency. The average time this sample of customers took was calculated to be 1.43 minutes and their standard deviation in times was calculated to be 0.40 minutes. At the .10 level of significance, can we conclude that the average time with the new ATM machines is different than the average time with the old ATM machines?

When completing each question, make sure that you have included:

• the two hypotheses
• the value of the test statistic along with your calculations
• the p-value of the test along with the appropriate graph
• the decision rule along with the appropriate graph
• a two-part conclusion: whether you reject or don’t reject the null hypothesis, and, what does this rejection mean to the particular question

Answer 1

Solution:

Given:

From the data, sample mean is = 1.43 and the Sample standard deviation is s = 0.40, and the sample size is n = 30.

Null and Alternative Hypotheses:

This corresponds to a two-tail test, for which a t-test for one mean, with unknown population standard deviation will be used.

Test statistic:

Formula:

The number of degrees of freedom are df = n-1 = 30-1=29

Rejection Region:
Given significance level = α = 0.10 and df = 29
The p-value can be found using excel formula, =TDIST(1.78,29,2)

P-value = 0.0855

Decision:

P-value < 0.10
It is then concluded that the Null Hypothesis is rejected.

Conclusion: It is concluded that the Null Hypothesis is not rejected. Therefore, there is enough evidence to claim that the population mean is different than 1.30 at the 0.10 significance level.

That is, the average time with the new ATM machines is different than the average time with the old ATM machines.

Done