A soft drink dispensing machine must be adjusted if the variance of the contents o² exceeds1.50 ml (ml² = squared milliliter). A random sample of 20 drinks from this machine has a varianceof 1.90 ml².Is it sufficient sample evidence that the machine must be adjusted?Test an appropriate hypothesis at a = 0.05. Assume that the contents dispensed by themachine are approximately normally distributed.a. State null and research hypotheses about population variance o².Ho:H₁b. Find the observed value of test statistic.Keep 3 digits after decimal point in the expression for observed value of test statistics.2The observed value of test statistic is bs.e. State the rejection region.The rejection region is X²c. Insert the word sufficient or insufficient into the following statement.There isbe adjusted._sample evidence to conclude that the machine must11

a. Suppose σ2 is the population variance of the contents of a soft-drink dispensing machine.

Answered: A soft drink dispensing machine must be…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A researcher takes sample temperatures in Fahrenheit of 16 days from San Francisco (Group 1) and 22 days from Atlanta (Group 2). Test the claim that the mean temperature in San Francisco is less than the mean temperature in Atlanta. Use a significance level of a = 0.10. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. Round answers to 4 decimal places. San Francisco 77.4 94.8 77 80.9 84 Ho: M₁ 73.4 84.9 92 60.6 83.6 92.5 76.3 93.4 87.2 81.5 70.4 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols for each of the 6 spaces. Atlanta 85.4 92.8 80.2 87.9 80.6 77.9 72.9 75.9 72.1 76.7 80.4 92.5 75.9 72.1 97.7 89.2 88.1 80 92.2 86 96.2 91.9 p-value H₁: M₁ Based on the hypotheses, find the following: Test Statistic = -0.635 X = 0.2494 × OH₂ The p-value is greater than alpha OF H₂ to alpha. The correct decision is to fail to reject the null hypothesis or The…
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular mu mu 1 mu 2 n 26 26 x overbar 0.79093 lb 0.81234 lb s 0.00433 lb 0.00753 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. Upper H 0 : mu 1 equalsmu 2 Upper H 1 : mu 1 greater thanmu 2 B. Upper H 0 : mu 1 equalsmu 2 Upper H 1 : mu 1 less thanmu 2 C. Upper H 0…
A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72 116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =
A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than .001 cm². The producer is required to test the bearings before they are shipped, and so the diameters of 16 bearings are measured with a precise instrument, resulting in the following values. Assume bearing diameters are normally distributed. Use the data and a = 0.01 to test to determine whether the population of these bearings is to be rejected because of too high a variance. 1.68 1.62 1.63 1.70 1.66 1.63 1.65 1.71 1.64 1.69 1.57 1.64 1.59 1.66 1.63 1.65 Appendix A Statistical Tables (Round your answer to 2 decimal places, e.g. 15.25.) The value of the test statistic is and we reject the null hypothesis ⇒
A sample tested the claim that heights of men and heights of women have difference variances, with s = 7.44592 cm for women and 7.12432 cm for men. The sample sizes are n₁ = 142 and n₂ = 159. When using the F test with these data, is it correct to reason that there is no need to check for normality because n₁ > 30 and n₂ > 30? Choose the correct answer below. O A. No. The F test has a requirement that samples be from normally distributed populations, regardless of how large the samples are. ⒸB. No. There is no need to check for normality regardless of the sample size. There is no normality requirement for the F test. O C. Yes. The F test has a requirement that samples be from normally distributed populations, but this requirement can be ignored for large samples (n, and no greater than 30). O D. No. There is no need to check for normality as long as n₁ ≥ 10 and n₂ ≥ 10.
The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use a = .10. a. State the null and alternative hypotheses. Ho: 0 12 equal to H : 0 1 ? not equal to 2 b. Calculate the value of the test statistic (to 2 decimals). c. The p-value is between .10 and .20 v d. What is your conclusion? Cannot conclude that the departments differ in terms of unit cost variance v
A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for samples of customer transactions for the two fast food restaurants are shown below. At x = 0.01, can you support the magazine's claim? Assume the population variances are equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below. Burger Stop Fry World X₁ = $11.22 X₂ = $10.59 $₁ = $0.79 $2 = $0.64 n₂ = 10 n₁ = 12 (a) Identify the claim and state Ho and H₂. Which is the correct claim below? O A. "The mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World." OB. "The mean amount spent by a customer at Burger Stop is equal to the mean amount spent by a customer at Fry World." O c. "The mean amount spent by a customer at Burger Stop is not equal to the mean amount spent by a customer at Fry World." O D.…
Two separate samples, each with 16 individuals, receive two different treatments. After treatment, the first sample has SS = 1540 and the second has SS = 1460. a. Find the pooled variance, s2p, for the two samples b. The estimated standard error is c. If the sample mean difference is 10 points (i.e., M1 - M2 = 10), compute the t-statistic. The t-statistic is:

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