**Statistical Analysis [1-7]**

**One-sample t-test**

A one-sample t-test can be used to test whether the sample mean is significantly different than a hypothesized value.

Copy and run the

__Example__Copy and run the

**CHIPS**data set from the yellow box below.The CHIPS data set contains 100 chips samples taken from ABC-branded chips.

On the nutrition label, the chips is shown to have 120 calories.

An inspection agency has randomly collected 100 chips samples to test whether the nutrition label shows the correct calories information.

A one-sample t-test is used to test the following hypothesis:

H0: µ=120

H1: µ≠120

where µ is the true and unknown chips calories.

The hypothesis testing can be performed using Proc ttest:

__Example__

Proc ttest Data=Chips H0=120;

Var Calories;

Run;

The

The following results are generated:

**H0**option specifies the hypothesized value to be tested.The following results are generated:

**1. Sampling Distribution**The first two table shows the

__sampling distribution of sample mean__such as mean, standard error and confidence limits.

The sampling distribution (of sample mean) has a mean of 138.2 and a standard error of 1.8729.

The 95% confidence limit is 134.5 to 142.

We can reject the null hypothesis since the 95% confidence interval does not contain the hypothesized value of 120.

**2. T-value and P-value**

The third table shows the t-value and p-value.

The p-value is less than 0.05.

This rejects the null hypothesis that the mean calories is 120.

**3. Histogram, box plot and Q-Q plot**

One of the main assumptions for one-sample t-test is that the dependent variable (i.e. calories) should be approximately normally distributed.

All the plots indicates the data is normally distributed.

**What does the result mean?**

The null hypothesis is rejected as the p-value is below 0.05.

There is sufficient evidence to reject the claim that the mean calories is 120.

The 95% confidence interval is [134.5, 142].

We are 95% certain the true mean calories is within this range.

The nutrition label is unlikely to be correct.

**Exercise**

The nutrition label also shows 135 mg of sodium in one serving.

Perform a one-sample t-test on whether the nutrition label shows the correct sodium information.

*Need some help?*

**HINT: **

The same one-sample t-test can be used to test the sodium information.

**SOLUTION: **

Proc ttest Data=Chips H0=135;

Var Sodium;

Run;

The p-value is again below 0.05. There is sufficient evidence to reject the hypothesis that 1 serving of chips contain 135 mg of sodium.

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