Question

1A technical magazine stated that the mean retail cost of all models of a particular laptop was $600. A random sample of 10 stores that sell that laptop in Los Angeles found it sold with a mean cost of $ 586.50 and a standard deviation of $26.77. Does this indicate that the mean cost of that laptop in Los Angeles is less than $ 600

Answer 1

Yes

Explanation:

Given,

Population mean Z = 600

Sample mean, µ = 586.50

Size of the sample, n = 10

Standard deviation, σ = 26.77

The testing hypothesis is,

Null hypothesis = µ<600

Alternative hypothesis = µ≥600

The test statistics is the calculated value of Z,

(Z- µ)/(σ/√n)

= (600-586.50)/(26.77/√10)

= (13.5*3.1623)/26.77

= 42.691/26.77

= 1.5947

And at 5% level of significance, the table value of Z = 1.644

Here, calculated Z<Table value of Z, so we accept the null hypothesis.

So, the null hypothesis is accepted. The mean value of the laptop is less than 600.