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
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ESSENTIALS OF STATISTICS 6TH ED W/MYSTA
- The proportion of adults living in a small town who are college graduates is estimated to be p = 0.5. To test this hypothesis, a random sample of 10 adults is selected. If the number of college graduates in the sample is anywhere from 3 to 7, we shall not reject the null hypothesis that p = 0.5; otherwise, we shall conclude that p + 0.5. Complete parts (a) through (c) below. Click here to view page 1 of the table of binomial probability sums. Click here to view page 2 of the table of binomial probability sums. Click here to view page 3 of the table of binomial probability sums. %3D (a) Evaluate a assuming that p = 0.5. Use the binomial distribution. (Round to four decimal places as needed.)arrow_forwardSuppose that arrival times at a certain emergency care center are following a Poisson process with a mean rate of λ= 0.2 arrivals per minute. Let T be the time until the third arrival. Find the mean and the variance of T, and find P(T ≤30) to four decimal places. Part 1 out of 3The mean of T is ________minutes.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 3.2 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_forward
- Assume that IQ scores are normally distributed with μ = 100 and σ = 15 What IQ score would be needed to score in the top 2% of IQ scores?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_forwardPlease review Section 11.1. Are you an impulse shopper? A survey of 1000 grocery shoppers indicated that 40% of males and 57% of females make an impulse purchase every time they shop. Assume that the survey consisted of 500 males and 500 females. Let group 1 be the males and let group 2 be the females.Ho : pie = pieH1 : pie /= pieCalculate the test statistic: (Round to three decimal places as needed.)Determine the critical value: (Round to three decimal places as needed.)State the Conclusion:arrow_forward
- Is this correct so far?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_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 3.7 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_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 3.5 3.9 4.0 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 5.1 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 (a) Assume that the crime rate distribution is approximately normal in both regions. Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (b) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1 − μ2. Do not use rounded values. Round your answer to three decimal places.) (c) Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limitarrow_forwardA sunscreen company is attempting to improve upon their formula so that it lasts in water longer. They have 4 lead scientists who each came up with a different formulas. In order to see if there is a difference in the time the sunscreen lasts the CEO collects a random sample of each of the four sunscreens the data is shown below. Test the claim that at least one sunscreen has a different lifespan in water at a 0.05 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 43 66 64 49 90 80 51 74 40 57 44 83 87 74 63 43 43 31 49 84 58 57 64 68 The hypotheses for this ANOVA test would be: Η 0: μ Αμ Bμσ μ p HA : At least one mean is different. (claim) α 0.05 Complete the ANOVA table below: (round answers to 3 decimal places) df MS F p-value Between 368.5 3 122.8333 0.410311 0.747339 Within 5987.333 20 299.8667 The decision of the test is to: reject Ho • do not reject Hoarrow_forwardA sunscreen company is attempting to improve upon their formula so that it lasts in water longer. They have 4 lead scientists who each came up with a different formulas. In order to see if there is a difference in the time the sunscreen lasts the CEO collects a random sample of each of the four sunscreens the data is shown below. Test the claim that at least one sunscreen has a different lifespan in water at a 0.05 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 81 75 52 79 77 34 40 87 64 39 32 72 47 43 61 58 57 47 48 46 80 43 38 63 The hypotheses for this ANOVA test would be: H0:μA=μB=μC=μDH0:μA=μB=μC=μD HA:HA: At least one mean is different. (claim) α=0.05α=0.05 Complete the ANOVA table below: (round answers to 3 decimal places) SS df MS F p-value Between Within The decision of the test is to: reject H0H0 do not reject H0H0 The final conclusion is: There is not enough evidence to reject the claim that…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill