Question

A nutritionist claims that children under the age of 10 years are consuming more than the U.S. Food and Drug Administration’s recommended daily allowance of sodium, which is 2300 mg. To test this claim, she obtains a random sample of 16 children under the age of 10, and measures their daily consumption of sodium. The mean amount of sodium consumed is 2500 mg with a standard deviation of 320 mg. Is there significant evidence to support the claim of the nutritionist at α = 0.05 level of significance? Assume the population is normally distributed.

The value of the test statistic for this hypothesis test is _________.

The critical value for this hypothesis test is _________.

The decision rule for this hypothesis test is that _________.

Answer 1

Given that, sample size ( n ) = 16

sample mean = 2500 mg

sample standard deviation = 320 mg

The null and alternative hypotheses are,

Test statistic is,

The value of the test statistic for this hypothesis test is 2.5

t-critical value at α = 0.05 level of significance with degrees of freedom = 16 - 1 = 15 is, t^* = 1.753

The critical value is 1.753

Decision rule : Reject H₀, if t > 1.753

Since, t = 2.5 > 1.753, we reject the null hypothesis (H₀).