In Exercises 5–20, assume that the two samples are independent simple random samples selected from
19. Is Old Faithful Not Quite So Faithful? Listed below are time intervals (min) between eruptions of the Old Faithful geyser. The “recent” times are within the past few years, and the “past” times are from 1995. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.05 or 0.01?
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Elementary Statistics (13th Edition)
- (All one question just could not fit into one picture)arrow_forwardAn alloy manufacturer is investigating if they can improve the strength of one of their alloysby producing it at a lower temperature. To investigate that, they produce the alloy at twodifferent temperatures (high and low) and then measure the breaking strength of randomsamples of specimens from each. The following table represents the strength of the randomsamples at the higher and lower temperature, in units of 0.001-inch deflection. Temp. Strength (0.001 inch)High 87 64 66 85 76 49 97 73 75 77 69 68 89 27 58 84Low 88 82 81 85 79 80 88 78 77 85 79 76 Do the results support the hypothesis that lowering the production temperature can improve thestrength of the alloy, with 95% confidence? (Hint: Don’t forget investigating variances. Use 98% confidence for that.)arrow_forwardplease solve question 21 and 23arrow_forward
- please answer part barrow_forwardA random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.2 3.1 4.0 3.2 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.7 4.1 4.5 5.1 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Note: If a two-sample t-test is appropriate, for degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (a) Do the data indicate that the violent crime rate in the Rocky Mountain…arrow_forwardSuppose data shows that only 50% of breast cancer patients can survive more than 5 years. You suspect the percentage is too low, so you'd like to conduct a study to examine this situation. What is the null and alternative hypothesis in this situation?arrow_forward
- II. Conduct a hypothesis test A research center claims that less than 50% of senior high school students in public schools in the Philippines have accessed the Internet using cellular phones. In a random sample of 100 SHS students, 39% say they have accessed the Internet using cellular phones. At = 0.01, is there enough evidence to support the researcher's claim?arrow_forward, 16. A statistically minded fraternity junior keeps records on how many girls he has to ask before one agrees to be his date for a Saturday football game. His school plays five home games and his five acceptances come on the 3rd, 6th, 4th, 2nd, and 9th girl he asks. Assume that the probability, e, that any girl he asks will accept his invitation is constant from girl to girl. Mind ML estimate of e.arrow_forward(iii) Find (or estimate) the P-value. OP-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005< P-value < 0.025 OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. O -4 -2 0 2 2 M 2 DO Q -2 -2 (iv) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there…arrow_forward
- A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.0 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.5 4.3 4.5 5.1 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to three decimal places.) x1 = s1 = x2 = s2 = (ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01.(a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)arrow_forwardA random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.9 4.2 4.1 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.7 4.1 4.7 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 <…arrow_forwardA random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.9 4.2 4.1 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.7 4.1 4.7 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 <…arrow_forward
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