Answer to Question #171055 in Statistics and Probability for Sowmya

Question

Over the last 3 years, Art's Supermarket has observed the following distribution of modes of payment in the express lines: cash (C) 41%, check (CK) 24%, credit or debit card (D) 26%, and other (N) 9%. In an effort to make express checkout more efficient, Art's has just begun offering a 1% discount for cash payment in the express checkout line. The following table lists the frequency distribution of the modes of payment for a sample of 500 express-line customers after the discount went into effect. Mode of payment CK Number of customers 240 104 111 45 Test at the 1% significance level whether the distribution of modes of payment in the express checkout line changed after the discount went into effect. Show the work for both classical approach and p-value approach. Make sure to show the work for the four steps diecused

Answer 1

$H_o$ : Current percentage distributions of modes of payment are

same as after discount went into effect.

$H_a$ :  Current percentage distributions of modes of payment are different from the distribution after discount went into effect.

$\chi_c^2=\sum\dfrac{(O-E)^2}{E}$

From the math we see that percentage distributions of modes of payment  are C = 41%, CK = 24%, D =26%, and N =9%. So, we use these distributions to calculate the expected frequency and the value

of chi-square test statistics.

so, $\chi^2_c=\sum \dfrac{(O-E)^2}{E}$

$=5.97+2.13+2.85=10.95$

Calculated value of $\chi_c^2$ is less than the standard value at 1% significance level i.e. 11.35

$\implies 10.95<11.35$

Fail to reject null hypothesis means that current distribution of modes of payment is same as after the discount effect went into effect. In fact, percentage distributions for modes of payment are same as before, and we are 99% confident about the result so far.