A machine that puts corn flakes into boxes is adjusted to put an average of 15.3 ounces into each box, with standard deviation of 0.23 ounce. If a random sample of 15 boxes gave a sample standard deviation of 0.36 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.) (i) Give the value of the level of significance. 0.01 State the null and alternate hypotheses. H0: σ2 = 0.0529; H1: σ2 ≠ 0.0529 H0: σ2 = 0.0529; H1: σ2 < 0.0529 H0: σ2 = 0.0529; H1: σ2 > 0.0529 H0: σ2 < 0.0529; H1: σ2 = 0.0529 (ii) Find the sample test statistic. (Round your answer to two decimal places.) 3.47 (iii) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005 (iv) Conclude the test. Since the P-value ≥ α, we fail to reject the null hypothesis. Since the P-value < α, we reject the null hypothesis. Since the P-value < α, we fail to reject the null hypothesis. Since the P-value ≥ α, we reject the null hypothesis. (v) Interpret the conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.
i) H0: σ2 = 0.0529; H1: σ2 > 0.0529
ii) sample test statistic =(n-1)*(S/σ)2 =(15-1)*(0.36/0.23)2 =34.30
iii)
P-value < 0.005
(iv)
Since the P-value < α, we reject the null hypothesis
(v)
. At the 1% level of significance, there is sufficient evidence to conclude that the variance has increased and the machine needs to be adjusted
A machine that puts corn flakes into boxes is adjusted to put an average of 15.3...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.8 ounces into each box, with standard deviation of 0.22 ounce. If a random sample of 10 boxes gave a sample standard deviation of 0.39 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.) (i) Give the value of the level of significance. State the null...
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2 = 47.1. However, a random sample of 18 colleges and universities in Kansas showed that x has a sample variance s2 = 86.8. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is...
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A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of eight cups of coffee from this machine show the average content to be 7.4 ounces with a standard deviation of 0.70 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance. What are we testing...
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The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 52 5 to 14 13.6% 75 15 to 64 67.1% 282 65 and older 12.1% 46 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
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