Happy Harvest Bread Company needs to determine whether a new advertising campaig

Question

Happy Harvest Bread Company needs to determine whether a new advertising campaign has increased its mean daily income.  The daily income for 50 randomly selected business days prior to campaign was recorded.  After the advertising campaign, the income for another 30 randomly selected days was recorded.     Let probability of making a type I error be 2.5%. Do these data provide sufficient evidence for the management to conclude that the mean income has increased by the advertising campaign?  A summary of the results of the two samples is shown below:

Sample Mean   Sample Standard Deviation Sample Size

Before Campaign $2255 215 50

After Campaign $2330 238 30

The appropriate null and alternative hypotheses are:

a. H0: 1 - 2 < 0    Ha: 1 - 2 > 0

b. H0: 1 - 2 = 0    Ha: 1 - 2 > 0

c. H0: 1 - 2 = 0    Ha: 1 - 2 < 0

d. H0: 1 - 2 > 0    Ha: 1 - 2 < 0

Explanation / Answer

The correct answer is: c. H0: 1 - 2 = 0    Ha: 1 - 2 < 0

Reason: Since Happy Harvest Bread Company needs to determine whether the new advertising campaign has increased its mean daily income or not, the null hypothesis should be that there is no significant difference between the mean income before and after the campaign i.e. H0: 1 - 2 = 0 and the alternative hypothesis should be that the mean daily income after the campaign will be greater than that before the campaign

i.e. Ha: 1 - 2 < 0 => 2 > 1

Thanks!

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