Question

Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Adam reads that the average speed that cars drive on the highway is 65 mph. t equals fraction numerator x with bar on top minus mu over denominator begin display style bevelled fraction numerator s over denominator square root of n end fraction end style end fraction The t-test statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place.

Answer 1

The t-test statistic is
`t = -0.697`

Explanation:

The test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the expected mean,
`\sigma` is the standard deviation and n is the size of the sample.

The sample standard deviation is 7.309.

This means that
`\sigma = 7.309`

Adam reads that the average speed that cars drive on the highway is 65 mph.

This means that
`\mu = 65`

60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph.

8 values, so
`n = 8`

The sample mean is:

`X = (60.5 + 63.2 + 54.7 + 51.6 + 72.3 + 70.7 + 67.2 + 65.4)/(8) = 63.2`

Test statistic:

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (63.2 - 65)/((7.309)/(√(8)))`

`t = -0.697`

The t-test statistic is
`t = -0.697`