BUSN603 Quantitative Analysis

(1)

Null and alternative hypothesis

Ha: µ=15.11

Hb ;µ> 15.11

(2)

One tailed test is needed since we are testing the hypothesis in one direction. <15.11 of interest at 0.05 level of significance. We are testing the possibility of a relationship in one direction ( (chen, 2020).

One tail actually provides more power to detect an effect in one direction by not testing the effect in the other direction.

Null hypothesis: No significant difference in means

Alternative hypothesis: there is significant increase in means

The null hypothesis argues that there is no significant difference in the average number of documents produced per hour even with the installation of a bigger monitor

The alternative hypothesis argues that the average no of documents produced per hour will increase significantly with the installation of a bigger monitor.

(3) Standard Deviation

Standard deviation is the measure of the amount of variation of a dispersed set of values.(Square root of Variance)

Higher STD indicates that the values are spread over a smaller range or they are close to the mean set.

A lower STD indicates that the values are spread over a wider range therefore they are not close to the mean set.

Standard deviation=2.666

Random Variable- A random variable is a variable whose value depends on a certain outcome or a random phenomenon.

The mean number of processed documents per hour.15.11

(4) Compare and contrast T-test and Z-test (smith, 2018).

T-test is mostly used when n<30

It is used to determine if there is a significant difference between means of two groups. While the Z-test is used when>30 and is used to determine whether two population means are different when the variances have been provided. And the sample size is greater than 30.

Level of significance.

The level of significance is 0.05

The level of significance simply shows the probability of the event occurring by chance.

If the level is low it means the probability of the chance occurring is low and we say that the event is significant.

Level of significance is small hence the vent is significant.

Degrees of freedom

Degrees of freedom=n-1

Hence its 20-1=19

Critical value

T 0.05,19=3.883

t=X-µ/S/Square root of mean.

t=15.11-15/2.666/square root of 20=0.184521738

 

0.184521738<3.883

Hence reject Ho

There is a significant increase in means.

Installation of a bigger monitor increase the production of the number of documents per hour.

Bell curve (anderson, 2020).

References

anderson, s. (2020, march 21). investopedia. Retrieved from www.investopedia.com: https;//www.investopedia.com

chen, J. (2020, jul 1). investopedia . Retrieved from investopedia.com: htpps;//www.investopedia.com

smith, s. (2018, june). sciencing. Retrieved from www.sciencing.com: https:// www.sciencing.com

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