Question

Consider the Holiday Toy company. The company manufactures and distributes its products to several retail outlets all over the world. In planning production levels for the upcoming winter season, Holiday must decide on how many units of each product to produce prior to knowing the actual demand. Holiday’s marketing director is hypothesizing baseline mean demand to be equal to or greater than 40 units per retail outlet.
A single, random sample is collected on the “potential demand” of 81 retail outlets, and the report shows a sample mean demand of 36 units per retail outlet. The population standard deviation is known to be 25 units (from previous research).
Perform a traditional single-sample hypothesis experiment to test that the marketing director’s belief is false (α=.05). Based on what you find, choose the answer below that has the correct information for this experiment.

A. Ho: π ≥ 40 ; H1: π < 40 The decision is to Fail to Reject Ho based on a Zobserved = -1.44
The conclusion is that there is sufficient evidence his claim is false
B. Ho: μ ≤ 40 ; H1: μ > 40 The decision is to Reject Ho based on a Zobserved = -1.645
The conclusion is that there is insufficient evidence his claim is false
C. Ho: μ = 40 ; H1: μ ≠ 40 The decision is to Reject Ho based on a Zobserved = -1.645
The conclusion is that there is sufficient evidence his claim is false
D. Ho: π ≤ 40 ; H1: π > 40 The decision is to Fail to Reject Ho based on a Zobserved = -1.44
The conclusion is that there is insufficient evidence his claim is false
E. Ho: μ ≥ 40 ; H1: μ < 40 The decision is to Fail to Reject Ho based on a Zobserved = -1.44
The conclusion is that there is insufficient evidence his claim is false

Answer 1

Null hypothesis

vs

Alternative hypothesis

We have given,

Population mean =40

Sample mean = 36

Population standard deviation=25

Sample size =81

Z test statistic formula is

=-1.44

Z critical value for left tailed alternative hypothesis is -1.645

Decision rule Reject H0 if Z calculated < z critical value

E. Ho: μ ≥ 40 ; H1: μ < 40 The decision is to Fail to Reject Ho based on a Zobserved = -1.44
The conclusion is that there is insufficient evidence his claim is false