Question

A study claimed residents in a suburb town spend at most 1.9 hours per weekday commuting to and from their jobs. A researcher believed commute times were now different and wants to test this claim by sampling 14 adults. Sample statistics for these 14 adults are: X = 2.2 $=0.7 Can the researcher support the claim that mean commuting time is more than 1.9 hours ? Test using a =.01.

Answer 1

There is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours

Explanation:

From the question we are told that

The population mean is
`\mu = 1.9 \ hr`

The sample mean is
`\= x = 2.2`

The standard deviation is
`\sigma = 0.7`

The sample size is
`n = 14`

The level of significance is
`\alpha = 0.01`

The null hypothesis is
`H_o : \mu = 1.9 \ hr`

The alternative hypothesis is
`H_a : \mu > 1.9 \ hr`

Generally the test statistics is mathematically represented as

`t = (\= x - \mu )/( (\sigma)/( √(n) ) )`

`t = ( 2.2 - 1.9 )/( (0.7 )/( √(14) ) )`

`t = 1.6036`

The p-value is obtained from the z-table, the value is

`p-value = P(t > 1.6036) = 0.054401`

Looking at the value of
`p-value \ and \ \alpha` we see that
`p-value > \alpha`

So we fail reject the null hypothesis

Hence we can conclude that there is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours