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A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink.What is the test statistic? Group of answer choices-.97-.74.79.47

Question

A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink.What is the test statistic? Group of answer choices-.97-.74.79.47

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Solution

To find the test statistic, we need to use the formula for a proportion hypothesis test. The formula is:

Z = (p̂ - p₀) / √((p₀ * (1 - p₀)) / n)

where:

  • p̂ is the sample proportion
  • p₀ is the hypothesized population proportion
  • n is the sample size

Given in the problem:

  • p̂ = 80 / 400 = 0.20 (20% of the sample liked the drink)
  • p₀ = 0.22 (we are testing if at least 22% of the population will like the drink)
  • n = 400 (the sample size)

Substituting these values into the formula:

Z = (0.20 - 0.22) / √((0.22 * (1 - 0.22)) / 400) Z = -0.02 / √((0.22 * 0.78) / 400) Z = -0.02 / √(0.1716 / 400) Z = -0.02 / √(0.000429) Z = -0.02 / 0.020716 Z = -0.965

So, the test statistic is approximately -0.97.

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