Question

Old	New
16	12
9	9
17	15
10	8
9	5
4	4
30	25
29	21

A researcher believes she has designed a keyboard that is more efficient to use than a standard keyboard. In order to help decide if this is the case, typing speeds were taken for 16 different people. Eight of them are assigned to use old key board, and the other eight people are assigned to use the new key board. The lengths of time, in minutes, for each of the people to type a pre-selected manuscript are listed below. Assume the two population distributions are normal. Use the data in the Table to determine if the original keyboard yields slower times. Use a significance level of α = 0.05. Assume the two group has the same unknown population variance

Answer 1

: Population Mean length of time to type a pre-selected manuscript with old(original) key board

: Population Mean length of time to type a pre-selected manuscript with new key board

Claim : Original key board yields lower times : Mean length of Time taken with old key board is more than new key board or - > 0

Null hypothesis : H_o : - = 0

Alternate Hypothesis : H_a : - > 0

Right Tailed test :

The population variances of the two groups assumed equal.

Sample mean

Sample Standard deviation s:

For Old Key Board

n₁ : Sample size =8

	Old:x1
	16	0.5	0.25
	9	-6.5	42.25
	17	1.5	2.25
	10	-5.5	30.25
	9	-6.5	42.25
	4	-11.5	132.25
	30	14.5	210.25
	29	13.5	182.25
Total	124		642
Sample Mean:	124/8 = 15.5

Sample Mean length time to type a  pre-selected manuscript : = 15.5

Sample standard deviation to type a  pre-selected manuscript : s₁

For new Key board

	New: x2
	12	-0.375	0.140625
	9	-3.375	11.39063
	15	2.625	6.890625
	8	-4.375	19.14063
	5	-7.375	54.39063
	4	-8.375	70.14063
	25	12.625	159.3906
	21	8.625	74.39063
	99		395.875
Sample Mean	99/8 = 12.375

Sample Mean length time to type a  pre-selected manuscript : = 12.375

Sample standard deviation to type a  pre-selected manuscript : s₂

Degrees of freedom : df = n₁ +n₂ -2 = 8+8-2 =14

=0.05

For right tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.2399 > 0.05:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that original keyboard yields slower times