Question 1 Of 2010 Points In An Article Appearing Today

Question 1 Of 2010 Pointsin An Article Appearing Intodays Healtha Wr

Question 1 of .0 Points In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. Compute the z or t value of the sample test statistic.

A.z = 1.645 B.t = 1.916 C.z = 1.916 D.t = -1.916

Paper For Above instruction

The question requires performing a hypothesis test to determine whether the average calories in a serving of popcorn differ from the claimed average of 75 calories. Given the sample data—a mean of 78 calories, a sample standard deviation of 7, and a sample size of 20—the appropriate test statistic must be calculated. Because the population standard deviation is unknown and the sample size is small (n

Calculating the test statistic involves the formula for the t-value:

t = (x̄ - μ₀) / (s / √n)

Where:

  • x̄ = 78 (sample mean)
  • μ₀ = 75 (hypothesized population mean)
  • s = 7 (sample standard deviation)
  • n = 20 (sample size)

Plugging in the values:

t = (78 - 75) / (7 / √20) = 3 / (7 / 4.4721) = 3 / 1.5651 ≈ 1.916

This value indicates that the test statistic is approximately 1.916. Since the test involves assessing whether the population mean differs from 75 (a two-tailed test), the relevant critical values are based on the degrees of freedom (df = n - 1 = 19). The options provided are a z-score of 1.645 and a t-score of 1.916. The t-value computed is approximately 1.916, matching option B.

Therefore, the correct answer is B.t = 1.916.

References

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