Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 14 10 11 12 10 22 13 12 7 12 25 21 14 8 11 6 The sample mean is x = 13.0%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ ≠ 28 ml/kg; H1: μ = 28 ml/kg; two-tailedH0: μ = 28 ml/kg; H1: μ < 28 ml/kg; left-tailed H0: μ = 28 ml/kg; H1: μ > 28 ml/kg; right-tailedH0: μ = 28 ml/kg; H1: μ ≠ 28 ml/kg; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail.
| 14 | 10 | 11 | 12 | 10 | 22 | 13 | 12 |
| 7 | 12 | 25 | 21 | 14 | 8 | 11 | 6 |
The sample
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
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