Question

A certain brand of cereal claims that the mean sodium content per serving is less than 235 mg and past research suggests that the standard deviation is 10 mg. You find that a sample of 53 cereal servings has a mean sodium content of 233 mg. Using a 0.10 significance​ level, what can you conclude about the​ brand’s claim?

1) What type of hypothesis test is​ this?

​2) State the hypotheses.

3) Calculate the value of the Test Statistic.

4) Calculate the​ P-Value.

5) What is the​ Decision?

​6) Write the interpretation.

Answer 1

Solution :

Let X be a random samples of sodium content in mg

We have given that

Sample mean : = 233 mg

Sample size : n = 53

Populatio Standard deviation () = 10 mg

Level of significance is : = 0.10

1) We use One sample Z-test ,

Alternative hypothesis is the one tailed hypothesis .

2) Hypothesis test :

Mean sodium content per serving is equal 235 mg

Mean sodium content per serving is less than 235 mg

Symbolically :

3) Formula of one sample z test statistic is:

Under Null hypothesis test statistic is

Z = -1.46

4) P value :

P - Value = 0.073

5) Decision :

If P value is less than , so reject H0 at % Level of significance.

Here , 0.073 < 0.10 , So we may reject H0 at 10% level of significance.

6) Interpretation :

Using the Decision criteria We may Reject the null hypothesis.

Since there is significant to reject the null hypothesis at = 0.10.

So claim of certain brand of cereal the mean sodium content per serving is less tha 235 mg is corect.

Minitab output :

One-Sample Z

Test of μ = 235 vs < 235
The assumed standard deviation = 10

N Mean SE Mean 90% Upper Bound Z P
53 233.00 1.37 234.76 -1.46   0.073