Let the exponential function be, \(y=b(a)^{t}\)

\(\text{At}\ t=0\)

\(600=b(a)^{0}\)

\(b=600\) And at \(t=1\)

\(630=600(a)^{1}\)

\(a=\ \frac{630}{600}\)

\(a=\ \frac{21}{20}\) Therefore, the exponential function is \(y=600(\frac{21}{20})^{t}\).

Question

asked 2020-11-26

An analysis of laboratory data collected with the goal of modeling the weight (in grams) of a bacterial culture after several hours of growth produced the least squares regression line \(\log(weight) = 0.25 + 0.61\)hours. Estimate the weight of the culture after 3 hours.

A) 0.32 g

B) 2.08 g

C) 8.0 g

D) 67.9 g

E) 120.2 g

asked 2021-03-02

\(\begin{array}{|c|c|} \hline Tension\ level & Non-smoker & Moderate\ smoker & Heavy\ smoker \\ \hline Hypertension & 20 & 38 & 28 \\ \hline No\ hypertension & 50 & 27 & 18 \\ \hline \end{array}\)

Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.

asked 2020-12-02

We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.

If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups?

Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data?

Relationship between protein concentration \((mg/mL)\) of duodenal secretions to pancreatic function as measured by trypsin secretion:

\([U/ \frac{kg}{hr}]\)

Tapsin secreton [UGA]

\(\leq\ 50\)

\(\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.7 \\ \hline 2 & 2.0 \\ \hline 3 & 2.0 \\ \hline 4 & 2.2 \\ \hline 5 & 4.0 \\ \hline 6 & 4.0 \\ \hline 7 & 5.0 \\ \hline 8 & 6.7 \\ \hline 9 & 7.8 \\ \hline \end{array}\)

\(51\ -\ 1000\)

\(\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.4 \\ \hline 2 & 2.4 \\ \hline 3 & 2.4 \\ \hline 4 & 3.3 \\ \hline 5 & 4.4 \\ \hline 6 & 4.7 \\ \hline 7 & 6.7 \\ \hline 8 & 7.9 \\ \hline 9 & 9.5 \\ \hline 10 & 11.7 \\ \hline \end{array}\)

\(>\ 1000\)

\(\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 2.9 \\ \hline 2 & 3.8 \\ \hline 3 & 4.4 \\ \hline 4 & 4.7 \\ \hline 5 & 5.5 \\ \hline 6 & 5.6 \\ \hline 7 & 7.4 \\ \hline 8 & 9.4 \\ \hline 9 & 10.3 \\ \hline \end{array}\)

asked 2020-12-30

The tables show the battery lives (in hours) of two brands of laptops.
a) Make a double box-and-whisker plot that represent's the data.
b) Identifity the shape of each distribution.
c) Which brand's battery lives are more spread out? Explain.
d) Compare the distributions using their shapes and appropriate measures of center and variation.

asked 2020-11-07

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:

\(\begin{array}{c} Gender \\ \hline Affilation & Male & Female \\ \hline Democrat & 300 & 600 \\ Republican & 500 & 300 \\ Other & 200 & 100 \\ \hline \end{array}\)

What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:

\(\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}\)

the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

asked 2020-11-07

asked 2021-02-02

The measure of the supplement of an angle is \(\displaystyle{40}^{{\circ}}\) more than three times the measure of the original angle. Find the measure of the angles. Instructions: Use the statement: " Let the original angle be x " to begin modeling the working of this question.

a) Write algebraic expression in terms of x for the following:

I) \(40^{\circ}\) more than three times the measure of the original angle

II) The measure of the Supplement angle in terms of the original angle, x

b) Write an algebraic equation in x equating I) and II) in a)

c) Hence solve the algebraic equation in

b) and find the measure of the angles.

asked 2021-03-07

\(\begin{array}{|c|c|} \hline Subject & (1) & (2) & (3) & (4) & (5) &(6) & (7) & (8) & (9) \\ \hline Black & 25.85 & 28.84 & 32.05 & 25.74 & 20.89 & 41.05 & 25.01 & 24.96 & 27.47 \\ \hline White & 18.28 & 20.84 & 22.96 & 19.68 & 19.509 & 24.98 & 16.61 & 16.07 & 24.59 \\ \hline \end{array}\)

Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.

asked 2021-02-06

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:

\(\begin{array}{c} & Crawling\ age \\ \hline Birth\ month & Mean & St.dev. & n \\ \hline January & 29.84 & 7.08 & 32 \\ May & 28.58 & 8.07 & 27 \\ September & 33.83 & 6.93 & 38\end{array}\)

Crawling age is given in weeks. Assume the data represent three independent simple random samples, one from each of the three populations consisting of babies born in that particular month, and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below

. \(\begin{array}{c}Source & Sum\ of\ squares & DF & Mean\ square\ F \\ \hline Groups & 505.26\\ Error & & &53.45\\ Total\end{array}\)

What are the degrees of freedom for the groups term?

asked 2021-01-19

a) The statistic \(X^{2}\), that is used to estimate the variance \(S^{2}\) of a random sample, has a Chi-squared distribution.

b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.

c) The Chi-squared distribution is used in hypothesis testing and estimation.

d) The Chi-squared distribution is a particular case of the Gamma distribution.

e)All of the above.