Question

Solve this word problem using step by step procedure: The math department at a local university has customarily advised students to purchase Calculator A. The manufacturer has recently released a new model, Calculator B, which is reputed to be more user-friendly. The faculty decided to determine if there is a difference in the time required to perform a certain common statistical calculation. Twelve students chosen at random are given drills with both calculators so that they are familiar with the operation of each type. Then the time they take to complete the test calculation on each device is measured in seconds (which calculator they are to use first is determined by some random procedure to control for any additional learning during the first calculations). To be clear, each student worked through a particular type of statistics problem with one calculator and then did a similar problem on the other calculator. For each student, the amount of time in seconds that they spent on the problem with each calculator was recorded. Is Calculator B likely to be a more effective device than Calculator A?

Student	CalculatorA	Calculator B
1	23	19
2	18	18
3	29	24
4	22	23
5	33	31
6	20	22
7	17	16
8	25	23
9	27	24
10	30	26
11	25	24
12	27	28

b) Please use step by step guidelines so I can follow in this excel problem: In the sheet entitled “Part 2 Question 7”, you will find the death rate (per 1,000 resident population) for random samples of counties in Alaska and Texas. Is the average death rate among Alaska counties likely to be lower than that among Texas counties?

Alaska	Texas
1.4	7.2
4.2	5.8
7.3	10.5
4.8	6.6
3.2	6.9
3.4	9.5
5.1	8.6
5.4	5.9
6.7	9.1
3.3	5.4
1.9	8.8
8.3	6.1
3.1	9.5
6	9.6
4.5	7.8
2.5	10.2
	5.6
	8.6

Answer 1

a) To test H₀ : Calculators A and B are equally effective i.e. H₀ : , where are the mean time for calculations using calculators A and B.

Vs H_a : Calculator B is more effective than A i.e.  H_a : (Mean time taken by B is less than that of A, hence is more effective)

Since the same student is made to use both the calculators, the observations are paired.Hence the test appropriate is paired t test.

Test statistic is given by,

t =

t = = 2.324.

Critical t for 11 df = 2.2.Since t = 2.324 > 2.2, H₀ is rejected at 5% level of significance.

Using excel,

The output is obtained as:

For the one sided paired t test, the p value obtained 0.02<0.05; There is not sufficient evidence to support the null hypothesis.Hence H₀ may be rejected at 5% level of significance.

We may conclude that calculator B is more effective than A, supporting the manufacturer's claim.

b)

To test H₀ : Average death rate of Alaska and Texas counties are equal i.e.  H₀ : , where are the average death rate of Alaska and Texas counties respectively

Vs H_a : Average death rate among Alaska counties is likely to be lower than that among Texas counties    i.e.  H_a :

Running an independent sample t test, assuming equal variances,

The output is obtained as:

  

For one sided t test, the p value obtained 0.000<0.05; There is not sufficient evidence to support the null hypothesis.Hence H₀ may be rejected at 5% level of significance. We may conclude that average death rate among Alaska counties is likely to be lower than that among Texas counties.