Question

A sales consultant for Herron Pharmaceuticals wished to confirm that their packet of 24 paracetamol tablets was cheaper at the retail level than their rival product. The sales consultant collected price data from two independent samples, of size 19 for Herron and 26 for the rival company. These yielded an average and variance for the retail price of Herron's product of 351 cents and 68 cents squared respectively, and 366 cents and 77 cents squared for the rival. Under the usual assumptions, determine an 80% confidence interval for the price difference (use Herron minus rival) stating only the lower limit of the interval in cents (round to the nearest whole number).

Answer 1

Solution :

The 80% confidence interval for the difference between two population means is given as follows :

Where, x̄1, x̄2 are sample means, n1, n2 are sample sizes, t(0.20/2, n1 + n2 -2) is critical t-value to construct 80% confidence interval and

(s1)² and (s2)² are sample variances.

We have,

Using t-table we get,

Hence, 80% confidence interval for the price difference is,

On rounding to nearest whole number we get,

= (-18, -12)

The lower limit of 80% confidence interval for the price difference is -18 cents.