A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond. This year 80 dealers were selected at random and telephoned regarding a new receiver. It was discovered that 38% of those receivers had been sold. Since 38% is less than 40%, does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed to sampling? Test at the 0.05 level. Computed z = -0.37.
A) Cut back production.
B) Do not cut back production.
C) Increase production.
D) None of the above.

Question

Quizplus · Accepted Answer

To determine whether the 2 percentage point difference can be attributed to sampling or not, we need to conduct a hypothesis test.

Null hypothesis: p ≥ 0.4 (40% of new equipment sold)
Alternative hypothesis: p < 0.4 (less than 40% of new equipment sold)

We will use a one-tailed z-test at the 0.05 level of significance.

The calculated z-score is -0.37.

The critical z-value (from the z-table or calculator) for a one-tailed test at the 0.05 level of significance is -1.645.

Since the calculated z-score of -0.37 is greater than the critical z-value of -1.645, we fail to reject the null hypothesis.

Therefore, we can conclude that there is not enough evidence to support the claim that production cutbacks are needed. The difference of 2 percentage points can be attributed to sampling variability.

Hence, the best choice is B: Do not cut back production.

A Manufacturer of Stereo Equipment Introduces New Models in the Fall