17. In a modeling agency, a researcher wishes to see if the average height of female models is less than 67 inches, as the coach claims. A random sample of 60 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At 𝛼 = 0.05, which of the following shows the appropriate rejection of the given problem?*A.B.C.
Question
17. In a modeling agency, a researcher wishes to see if the average height of female models is less than 67 inches, as the coach claims. A random sample of 60 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At 𝛼 = 0.05, which of the following shows the appropriate rejection of the given problem?*A.B.C.
Solution
To answer this question, we need to conduct a one-sample t-test. Here are the steps:
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State the hypotheses. The null hypothesis is that the average height of female models is 67 inches. The alternative hypothesis is that the average height is less than 67 inches.
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Calculate the test statistic. The formula for the t statistic is (sample mean - population mean) / (standard deviation / sqrt(sample size)). Plugging in the given values, we get (65.8 - 67) / (1.7 / sqrt(60)) = -5.24.
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Determine the critical value. Since we are conducting a one-tailed test at 𝛼 = 0.05, we look up the critical value in a t-distribution table with 59 degrees of freedom (sample size - 1). The critical value is approximately -1.67.
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Compare the test statistic to the critical value. Since -5.24 is less than -1.67, we reject the null hypothesis.
So, the appropriate rejection of the given problem is that the average height of female models is less than 67 inches.
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