Question

The following data gives the mineral content (mg) of 8 randomly selected spinach samples. Does the data provide statistically significant evidence that the typical mineral content is less than 20.5 mg?

20.7, 20.1, 19.5, 20.0, 19.0, 21.8, 20.3, 18.9

Answer 1

From given data

= X / n = 20.0375

S = sqrt [ X2 - n 2 / ( n -1) ] = 0.9471

The null and alternative hypothesis are

H0: 20.5

Ha: < 20.5

Test statistics

t = ( - ) / (S / sqrt( n ))

= ( 20.0375 - 20.5) / ( 0.9471 / sqrt(8) )

= -1.38

t critical value at 0.05 significance level with 7 df = -1.895

Since test statistics falls in non-rejection region, we fail to reject H0.

We concldue that we do not have sufficient evidence to support the claim.