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### Question

Soft Drink Consumption. A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Find the P-value for the test. On the basis of the P-value, is the researcher’s claim valid?

### Answer #1 for Questions: Soft Drink Consumption. A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Find the P-value for the test. On the basis of the P-value, is the researcher’s claim valid?

**Answer:**

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### Answer #2 for Questions: Soft Drink Consumption. A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Find the P-value for the test. On the basis of the P-value, is the researcher’s claim valid?

**Answer:**

The null and alternative hypotheses are,

(The yearly consumption of soft drinks per person is 52 gallons.)

(The yearly consumption of soft drinks per person is not 52 gallons.)

Let the level of significance be.

Let the number of persons in a sample be.

Let the sample mean be.

Let the known standard deviation be.

Since, is known and the sample size is large, one sample z test is used.

The test statistic is,

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