Question

Please answer Part B and show all calculations (How you got the Standard Deviation, etc. )

(3) Website design options include mobile-first (structured to optimize performance for users on phones and mobile devices) and responsive design (structured to optimize performance for users on desktop computers).

Data were collected based on a random sample of the number of times users complained about website design on a given day. Five non-profit organizations with mobile-first design were studied, as well as six non-profit organizations with responsive design. The organizations are roughly comparable in terms of number of visitors and target audience. Data for each organization are shown below.

Non-profit organizations with mobile-first design (n = 5)
Non-profit number	1	2	3	4	5
Number of complaints per day	36 Variance =	65 Variance =	56 Variance =	50 Variance =	51 Variance =

Non-profit organizations with responsive design (n = 6)
Non-profit number	1	2	3	4	5	6
Number of complaints per day	81	76	78	53	52	78

(b) Conduct a hypothesis test with a = 0.05, estimating the t-statistic and the p-value.

Answer 1

B) Conduct a hypothesis test with a = 0.05, estimating the t-statistic and the p-value:

Here, Two independent samples are Five non-profit organizations with mobile-first design were studied, as well as six non-profit organizations with responsive design.

Therefore we use Two sample t-test

Set Hypothesis:

H0: M1 = M2

Ha: M1 ≠ M2

Where, M1 is Five non-profit organizations with mobile-first design, M2 is six non-profit organizations with responsive design.

Calculate Two Sample t-test:

Formula,

Where,

  

Table for caluclation:

S.N.	X1	X2	(X1-X1_bar)^2	(X2-X2_bar)^2
1	36	81	243.36	128.44
2	65	76	179.56	40.11
3	56	78	19.36	69.44
4	50	53	2.56	277.78
5	51	52	0.36	312.11
6		78		69.44
Sum	258	418	445.2	897.33
Mean	51.60	69.67

First calculate S2;

Then Calculate t-statistic,

( where we take Absolute value)

Calculate P-Value: (by using Excel)

we calculate p-value with (n1+n2 - 2 = 11-2 = 9) df and alpha=0.05 by using excel function TDIST(2.44,9,2) is,

P-value = 0.0372.

Decision: P-value (0.0372) is less than 0.05 then we reject h0.

Conclusion: M1 ≠ M2

There is difference between complaint of Five non-profit organizations with mobile-first design and six non-profit organizations with responsive design.