In testing a hypothesis about two population means, it the t distribution is used, which of the following assumptions is required? a Both populations are normally distributed. b Both population means are the same c The samples size are equal d The standard deviation are not the same
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In testing a hypothesis about two population means, it the t distribution is used, which of the following assumptions is required?
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a
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Both populations are
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b
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Both population means are the same
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c
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The
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d
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The standard deviation are not the same
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- An experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. The mean tip percentages and standard deviations are given in the accompanying table along with the sample sizes. 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). State the conclusion for the test. ID No candy Two candies H FFF H₁ H₂ b. Construct the confidence interval suitable for testing the claim in part (a). 14-₂0 < (Round to two decimal places as needed.) n x S 24 18.43 1.55 24 20.57 2.33 OA. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that giving candy does result in greater tips. B. Reject the null hypothesis. There is sufficient evidence to support the claim that giving candy does result in greater tips. OC. Fail to reject the null hypothesis. There is sufficient…Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Refer to the accompanying data set. Use a 0.01 significance level to test the claim that women and men have the same mean diastolic blood pressure. Women Men Women Men69.0 71.0 63.0 63.095.0 65.0 73.0 81.079.0 68.0 57.0 92.065.0 61.0 59.0 80.071.0 65.0 79.0 89.080.0 71.0 72.0 63.059.0 58.0 70.0 72.051.0 40.0 64.0 79.072.0 66.0 66.0 76.087.0 65.0 84.0 57.067.0 81.0 55.0 67.059.0 75.0 76.0 84.073.0 53.0 74.0 71.063.0 77.0 51.0 69.066.0 51.0 91.0 68.087.0 91.0 58.0 71.057.0 78.0 82.0 73.085.0 81.0 83.0 72.071.0 59.0 77.0 68.062.0 73.0 66.0 77.071.0 80.0 72.0 67.072.0 103.0 61.0 51.089.0 61.0 88.0 66.070.0 79.0 57.0 71.067.0 73.0 77.0 66.067.0 84.0 77.0 76.071.0 64.0 90.0 51.081.0 67.0 64.0 55.073.0 55.0 70.0 65.089.0 84.0 79.0 85.063.0 78.0 42.0 84.069.0 56.0 73.0 72.077.0 62.0 71.0 80.091.0 65.0 46.0…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 a = 0.05, 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 = $8.14 X2 = $7.51 s = $0.84 S2 = $0.79 n1 = 13 n2 = 11 (a) Identify the claim and state H, and Ha. Which is the correct claim below? O A. "The mean amount spent by a customer at Burger Stop is equal to the mean amount spent by a customer at Fry World." O B. "The mean amount spent by a customer at Fry World is greater than the mean amount spent by a customer at Burger Stop." OC. "The mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World." O D. "The…
- Consider two populations in the same state. Both populations are the same size (22,000). Population 1 consists of all students at the State university. Population 2 consists of all residents in a small town. Consider the variable Age. Which population would most likely have the largest standard deviation? They would likely have the same standard deviation(SD) for age because they have the same population size. O Population 2 would more likely have a higher standard deviation (SD) than Population 1. Population 1 would more likely have a higher standard deviation(SD) than Population 2 There is not enough information to tell.Is race a factor in the number of times a month a person eats out? The table below shows data that was collected. Asian 8 13 4 10 3 6 4 11 0 White 6 1 7 8 13 7 8 Ho: ₁1₂= μ3 = μ₁ H₁: At least two of the means differ from each other. Assume that all distributions are normal, the four population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of a = 0.1. 1. For this study, we should use Select an answer 2. The test-statistic for this data = 3. The p-value for this sample= 4. The p-value is Select an answer 5. Base on this, we should Select an answer 6. As such, the final conclusion is that... Black 9 5 6 10 8 14 6 Hispanic 12 10 8 8 12 7 0 (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) hypothesis O There is insufficient evidence to support the claim that race is a factor in the number of times per month people eat out. V α O There is sufficient evidence to support the…2. Which of the following are practical ways to assess normality of the residuals? Select all that apply a. Normal probability plots (the R command is qqnorm() b. Anderson-Darling tests. c. Shapiro-Wilks tests. d. Boxplots e. Just ask if they are normal, or, guess, because, who really cares?
- In a recent year, 11th grade New York public school students taking an English test produced test scores that were normally distributed with a mean of 84 and a standard deviation of 7.2. Let x be a random variable that represents a test score. What is the lowest score that would still place a student in the top 30% of the scores? A. 85.82 B. 87.78 C. 82.52 D. 79.47A 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 =Listed in the accompanying table are waiting times (seconds) of observed cars at a Delaware inspection station. The data from two waiting lines are real observations, and the data from the single waiting line are modeled from those real observations. 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). One Line Two Lines 64.1 733.6 64.3 865.2 157.2 605.8 215.8 1089.7 142.2 267.8 85.6 662.7 278.9 310.2 339.6 518.1 253.2 128.8 199.5 565.6 475.7 132.9 630.3 268.2 478.2 122.1 333.1 350.4 473.5 128.9 328.9 95.2 402.1 232.7 914.6 99.7 721.6 461.2 552.8 162.7 760.7 482.2 596.7 100.6 692.3 518.1 837.1 508.5 903.1 580.2
- Suppose that you want to perform a hypothesis test for a population mean. Assume that the population standard deviation is unknown and that the sample size is relatively small. In each part, the distribution shape of the variable under consideration is given. Decide whether you would use the t-test, the Wilcoxon signed-rank test, or neither. a. Triangular b. Symmetric bimodal c. Left skewedMale BMI Female BMI se H2 47 Given in the table are the BMI statistics for random samples of men and women. 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. n 47 26.3343 27.3646 8.781948 se 5.636805 se What are the null and alternative hypotheses? se O B. Ho H1 = H2 H1 H1 #H2 O A. Ho H1 H2 H1: H1 H2 O D. H, H1 #H2 H1: H1 < H2 se The test statistic, t, is. (Round to two decimal places as needed.) se The P-value is (Round to three decimal places as needed.)Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. College A 3.7 3.2 3.0 2.5 2.7 3.6 2.8 3.4 College B 3.8 3.2 3.0 3.9 3.8 2.5 3.9 2.8 4.0 3.6 2.6 4.0 3.6 Construct a 95% confidence interval for μ1−μ2, the difference between the mean GPA of college A students and the mean GPA of college B students. Round to two decimal places. (Note: x1=3.1125, x2=3.4385, s1=0.4357 s2=0.5485
