A random sample of n1 = 55 stemmed projectile points showed the mean length to be x1 = 3.00 cm, with sample standard deviation s1 = 0.80 cm. Another random sample of n2 = 46 stemless projectile points showed the mean length to be x2 = 2.70 cm, with s2 = 0.90 cm. Do these data indicate a difference (either way) in the population mean length of the two types of projectile points? Use a 5% level of significance. What are we testing in this problem? A or b? A.difference of proportionsdifference of means b. paired differencesingle meansingle proportion What is the level of significance? State the null and alternate hypotheses, which one? a.H0: ?1 ≠ ?2; H1: ?1 = ?2 B.H0: ?1 ≤ ?2; H1: ?1 > ?2 C. H0: ?1 = ?2; H1: ?1 ≠ ?2 D.H0: ?1 ≥ ?2; H1: ?1 < ?2 What sampling distribution will you use? What assumptions are you making? a.The standard normal. We assume that both population distributions are approximately normal with known population standard deviations. b.The Student's t. We assume that both population distributions are approximately normal with known population standard deviations. C.The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations. d.The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to three decimal places.) Estimate the P-value:which one below? P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? Which one correct? A. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. b.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. C. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. d.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. Interpret your conclusion in the context of the application. A.There is sufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points. b.There is insufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points.

A random sample of n1 = 55 stemmed projectile points showed the mean length to be x1 = 3.00 cm, with sample standard deviation s1 = 0.80 cm. Another random sample of n2 = 46 stemless projectile points showed the mean length to be x2 = 2.70 cm, with s2 = 0.90 cm. Do these data indicate a difference (either way) in the population mean length of the two types of projectile points? Use a 5% level of significance. What are we testing in this problem? A or b? A.difference of proportionsdifference of means b. paired differencesingle meansingle proportion What is the level of significance? State the null and alternate hypotheses, which one? a.H0: ?1 ≠ ?2; H1: ?1 = ?2 B.H0: ?1 ≤ ?2; H1: ?1 > ?2 C. H0: ?1 = ?2; H1: ?1 ≠ ?2 D.H0: ?1 ≥ ?2; H1: ?1 < ?2 What sampling distribution will you use? What assumptions are you making? a.The standard normal. We assume that both population distributions are approximately normal with known population standard deviations. b.The Student's t. We assume that both population distributions are approximately normal with known population standard deviations. C.The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations. d.The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to three decimal places.) Estimate the P-value:which one below? P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? Which one correct? A. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. b.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. C. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. d.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. Interpret your conclusion in the context of the application. A.There is sufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points. b.There is insufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

A random sample of n₁ = 55 stemmed projectile points showed the mean length to be x₁ = 3.00 cm, with sample standard deviation s₁ = 0.80 cm. Another random sample of n₂ = 46 stemless projectile points showed the mean length to be x₂ = 2.70 cm, with s₂ = 0.90 cm. Do these data indicate a difference (either way) in the population mean length of the two types of projectile points? Use a 5% level of significance.

What are we testing in this problem? A or b?

A.difference of proportionsdifference of means b. paired differencesingle meansingle proportion

What is the level of significance?

State the null and alternate hypotheses, which one?

a.H₀: ?₁ ≠ ?₂; H₁: ?₁ = ?₂

B.H₀: ?₁ ≤ ?₂; H₁: ?₁ > ?₂

C. H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂

D.H₀: ?₁ ≥ ?₂; H₁: ?₁ < ?₂

What sampling distribution will you use? What assumptions are you making?

a.The standard normal. We assume that both population distributions are approximately normal with known population standard deviations.

b.The Student's t. We assume that both population distributions are approximately normal with known population standard deviations.

C.The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations.

d.The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations.

What is the value of the sample test statistic? (Test the difference ?₁ − ?₂. Round your answer to three decimal places.)

Estimate the P-value:which one below?

P-value > 0.500

0.250 < P-value < 0.500
0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? Which one correct?

A. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

b.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

C. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

d.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Interpret your conclusion in the context of the application.

A.There is sufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points.

b.There is insufficient evidence at the 0.05 level to conclude that there is a difference in mean length of the two types of projectile points.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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