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 2400mg. To test the claim, she obtained a random sample of 75 children under the age of 10 and measured their daily consumption of sodium. The sample mean amount of sodium consumed was 2993 mg and the sample standard deviation was 1889 mg. Is there significant evidence to support the nutritionist’s claim that the mean amount of sodium consumed by children under the age of 10 years is more than 2400mg at α = 0.05? Step 1) State the null and alternative hypotheses. Step 2) Check the assumptions. Step 3) State the level of significance. Step 4) Compute the test statistic. Step 5) Compute the p-value. Step 6) Decide whether you reject H0 or fail to reject H0 using the p-value approach. Step 7) State your final conclusion in the context of the problem.

Answer 1

Step 1: Here claim is that mean is greater than 2400

So hypothesis is vs

Step 2: Here n>30, so we will use z test statistics

.Step 3: Level of significance is 0.05

Step 4: Test statistics is

Step 5: P value is

Step 6: As P value is less than alpha=0.05, we reject the null hypothesis

Step 7: We have sufficient evidence to support the claim that mean is greater than 2400