1. Consider the following autocorrelation plot: 1.00 Autocorrelations -0.50 10 20 Lag Bartlett's formula for MA(q) 95% confidence bands 0 Autocorrelations 30 40 (a) Approximately, what is the estimated 20th order autocorrelation? Is it statistically significantly different from 0? (b) An AR(1) model is proposed to fit this data. Again approximately, what would be the estimated coefficient on the lagged value of y? (c) What kind of autocorrelation function must an AR(1) model produce?

1. Consider the following autocorrelation plot: 1.00 Autocorrelations -0.50 10 20 Lag Bartlett's formula for MA(q) 95% confidence bands 0 Autocorrelations 30 40 (a) Approximately, what is the estimated 20th order autocorrelation? Is it statistically significantly different from 0? (b) An AR(1) model is proposed to fit this data. Again approximately, what would be the estimated coefficient on the lagged value of y? (c) What kind of autocorrelation function must an AR(1) model produce?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Consider the data in the table in Ex 9.16. (photo attached) Does the data provide significant evidence at the 3.9% level, to indicate that the population mean time among schizophrenics exceeds the population mean time among normal individuals by more than 15.0?(zobs =3.612, z.039 =1.76 )
A study was designed in which the relationship between smoking and work status was examined with 99% confidence. The table obtained for this purpose is as attached. Which of the following is wrong?A. With 99% confidence, no statistically significant relationship was found between smoking and work status.B. H0: There is a relationship between smoking and job status.C. Chi-square table value = 6.63D. Calculated Chi-square value approximately = 3.079
11. Consider the following autocorrelation plot: 1.00 0.50 Autocorrelations of y 0.00 -0.50 0 20 Lag Bartlett's formula for MA(q) 95% confidence bands Autocorrelations 10 30 40 (a) Approximately, what is the estimated 20th order autocorrelation? Is it statistically significantly different from 0? (b) An AR(1) model is proposed to fit this data. Again approximately, what would be the estimated coefficient on the lagged value of y? (c) What kind of autocorrelation function must an AR(1) model produce?
Stephen Stigler determined in 1977 that the speed of light is 299,710.5 km/sec. In 1882, Albert Michelson had collected measurements on the speed of light ("Student t-distribution," 2013). His measurements are given in table #7.3.6. Is there evidence to show that Michelson’s data is different from Stigler’s value of the speed of light? Test at the 5% level. Table #7.3.6: Speed of Light Measurements in (km/sec) 299883 299816 299778 299796 299682 299711 299611 299599 300051 299781 299578 299796 299774 299820 299772 299696 299573 299748 299748 299797 299851 299809 299723
In the regression equation, ŷ = 2.164 + 1.3657x, and n = 6, the mean of x is 8.667, SSxx= 89.333 and Se= 3.44. A 95% confidence interval for the average of y when x=8 is ______. a) (9.13, 17.05) b) (2.75, 23.43) c) (10.31, 15.86) d) (3.56, 22.62) e) (12.09, 14.09)
2. The following passage is from a paper. Also significant was the proportion of males and their water consumption (8 oz. servings) compared to females (X2 = 8.136, P-value = 0.087). Males came closer to meeting recommended daily water intake (64 oz. or more) than females (29.8% vs. 20.9%). This statement was based on carrying out a chi-square test of homogeneity using data in a two-way table where rows corresponded to sex (male, female) and columns corresponded to number of servings of water consumed per day, with categories none, one, two to three, four to five, and six or more. A) What hypotheses did the researchers test? H0: Sex and number of servings of water consumed per day are not independent. Ha: Sex and number of servings of water consumed per day are independent. H0: The proportions falling into each of the water categories are the same for both sexes.Ha: The proportions falling into each of the water categories are not the same for both sexes. H0: The…
2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ = 10 inches? (Use α = 0.05)
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 7.4 7.7 9.7 8.1 8.7 6.3 7.8 11.6 9.0 7.7 6.8 7.9 11.3 6.8 8.7 5.8 7.3 7.2 7.8 9.7 7.0 11.8 7.1 10.7 6.5 7.0 6.3 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex; = 219.7.] (Round your answer to three decimal places.) MPа State which estimator you used. O s/x (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPа State which estimator you used. s/X O
In simple linear regression, at what value of the independent variable, X, will the 95% confidence interval for the average value of Y be narrowest? At what value will the 95% prediction interval for the value of Y for a sin gle new observation be narrowest?
What is the approximate prediction interval for Y using an alpha of 5%? (Round answer to 3 decimal places.)
The mean exam score for 44. male high school students are 19.9 and the population standard deviation is 5.2. The mean exam score for 55female high school students is 19.4 and the population standard deviation is 4.9. At α=0.01, can you reject the claim that male and female high school students have equal exam scores? Complete parts (a) through (e). (a) Identify the claim and state H0 and Ha. What is the claim? A. Male high school students have lower exam scores than female students. B. Male and female high school students have different exam scores. C. Male and female high school students have equal exam scores. D. Male high school students have greater exam scores than female students. What are H0 and Ha? Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.