First interpretation of bank statement: The bank does not know whether the “mean dollars spent per card holder per month online” is GREATER than ( > ) the “mean dollars spent per card holder per month” at clothing stores.

and

Second interpretation of bank statement: The bank does not know whether the proportion of customers shopping online is GREATER than ( > ) the proportion of customers shopping at clothing stores.

Let us now proceed to talk about how you would analyze SAMPLE DATA COLLECTED for the first interpretation.

ANALYSIS PROCEDURE FOR THE FIRST INTERPRETATION OF THE BANK STATEMENT:

The first interpretation requires the use of “Welch’s parametric approximate t method” for inference on two independent samples.

‡WELCH’S METHOD SIX STEPS FOR THE FIRST INTERPRETATION OF THE BANK STATEMENT ARE AS FOLLOWS:

1) A claim is made regarding two population means “μ1 = online mean dollars spent per card holder per month online” and “μ2 = clothing store mean dollars spent per card holder per month”.

The claim is constructed to determine the null (Ho) and alternative (H1) or (Ha) hypothesis.

2) The level of significance “α” is determined based on how the bank perceives the seriousness of making a Type I error. Type I error occurs when we reject Ho and Ho is true.

3) Two independent samples would be taken from the bank’s current card holder population where the two independent sample sizes “n1” and “n2” are large, i.e. n1 ≥ 30 & n2 ≥ 30.

4) A normal probability plot and boxplot is made on each independent sample n1 & n2 to ensure that Welch’s parametric approximate t method can be used.

If a normal probability plot indicates that sample data collected is NOT normally distributed or a boxplot indicates outliers then a nonparametric test would be required.

**FOR THE ASSIGNMENT WE WILL ASSUME THAT WELCH’S APPROXIMATE T WILL BE VALID FOR THE FIRST INTERPRETATION OF THE BANK STATEMENT.**

5) A critical t-value or t-score is determined using Table III in the rear of your textbook based on the assigned level of significance “α” and on the sample size providing the smaller degrees of freedom “n1 -1 “ or “n2 – 1”.

6) Lastly, the “test statistic t” is calculated and compared to the critical t-value arriving to a conclusion to either REJECT or NOT TO REJECT the null (Ho) hypothesis.

Let us now proceed to talk about how you would analyze SAMPLE DATA COLLECTED for the second interpretation.

ANALYSIS PROCEDURE FOR THE SECOND INTERPRETATION:

The second interpretation requires using “parametric inference on two population proportions”..

‡THE SIX STEPS FOR INFERENCE ON TWO POPULATION PROPORTIONS ARE AS FOLLOWS:

1) A claim is made regarding two population proportions “P1 = proportion of card holders that shop online” and “P2 = proportion of card holders that shop at a clothing store”.

The claim constructed is used to determine the null (Ho) and alternative (H1) or (Ha) hypothesis.

2) The level of significance “α” is decided based on how the bank perceives the seriousness of making a Type I error. Type I error occurs when we reject Ho and Ho is true.

3) Two independent samples would be obtained from the bank’s current card holder population utilizing simple random sampling where the sample sizes are no more than 5% of the population size.

Since the bank presumably will offer its new card nation wide, the population size “N” would be in the MILLIONS.

4) We would check on both samples that the condition “nP(1-P)≥ 10” is met where “n” is the sample size and “P” is the sample proportion.

***FOR THE ASSIGNMENT WE WILL ASSUME THAT THE PARAMETRIC INFERENCE ON TWO POPULATION PROPORTIONS WILL BE VALID FOR THE SECOND INTERPRETATION OF THE BANK STATEMENT.***

5) A critical z-value would be determined using Table II in the front of your textbook based on the assigned level of significance “α”.

The critical z-value is determined by matching the non-critical region area “1-α” provided in Table II to its appropriate z-value or z-score.

6) Lastly, the “test statistic Z” would be calculated using the “pooled estimate of proportion P” and compared to the critical z-value arriving to a conclusion to either REJECT or NOT TO REJECT the null (Ho) hypothesis.

This is what I have come up with so far but I dont understand what to do next

Piggybank wishes us to determine whether the “mean dollars spent per card holder per month online” is GREATER than ( > ) the “mean dollars spent per card holder per month” at clothing stores.

m 1 is the mean dollars spent per card holder per month online

m 2 is the mean dollars spent per card holder per month at clothing stores.

We then can formulate the hypotheses:

H0: m 1 - m 2 = 0 verse HA: m 1 - m 2 > 0.

and

Piggybank wishes us to determine whether the “proportion of card holders that shop online” is GREATER than ( > ) the “proportion of card holders that shop at a clothing store”.

P1 = proportion of card holders that shop online

P2 = proportion of card holders that shop at a clothing store.

We then can formulate the hypotheses:

H0: (P1-P2) = 0 against the alternative HA: (P1– P2) > 0

Please advise