8.44 The mean time taken to design a house plan by 40 architects was found to be 23 hours with a standard deviation of 3.75 hours.
a. Construct a 98% confidence interval for the population mean μ.
b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Describe all possible alternatives. Which alternative is the best and why?
In: Math
16. In a study of the effect of prenatal cocaine use on infants, the following sample data were obtained for weights at birth: n = 101, x 2700 grams , and s = 645 grams (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et al., Journal of the American Medical Association, Vol. 291, No. 20). Use the sample data to construct a 95% confidence interval estimate of the standard deviation of all birth weights of infants born to mothers who use cocaine during pregnancy. Round to the nearest whole gram.
In: Math
Use the following to answer 5 - 8.
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the .05 significance level, test the claim that the sample of 1000 subjects has distribution that agrees with the distribution of state populations.
5.) Which of the following is the correct statement for the claim?
H1: Wa = .51, Or = .3, Id = .11, Mn= .08 |
Ho: At least one of the percentages is different |
H1: At least one of the percentages is different. |
Ho: Wa = .51, Or = .3, Id = .11, Mn= .08 |
6.) The test statistic is:
33.942 |
31.938 |
26.963 |
17.455 |
7.) The p-value is:
.000000238 |
.000000539 |
.000000989 |
.263122245 |
8.) The conclusion for this test is:
Fail to reject Ho which says there is sufficient evidence to warrant rejection of the claim of the same distribution |
Reject Ho which says there is sufficient evidence to support the claim of the same distribution |
Fail to reject Ho which says that there is sufficient evidence to support the claim of the same distribution |
Reject Ho which says there is sufficient evidence to warrant rejection of the claim of the same distribution |
In: Math
I'm doing a stats project on the correlation between the amount of hours a person sleeps and their weight; proving there is no correlation between sleep and weight gain. I have voluntary samples of people's weight and the hours they slept, and I need to list if the level of measurement is nominal or ordinal, confidence interval, and linear correlation test. how do I do this?
In: Math
Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.
Hotel A | Hotel B | Hotel C | |
Sample average ($) | 135 | 160 | 105 |
Sample standard deviation | 17.2 | 22.2 | 12.1 |
(a) Find a 95% confidence interval for the difference in the
average room rates for the Hotel A and the Hotel C chains. (Round
your answers to two decimal places.)
$ to $
(b) Find a 99% confidence interval for the difference in the
average room rates for the Hotel B and the Hotel C chains. (Round
your answers to two decimal places.)
$ to $
(c) Do the intervals in parts (a) and (b) contain the value
(μ1 − μ2) = 0?
Yes, the interval in part (a) contains (μ1 − μ2) = 0.Yes, the interval in part (b) contains (μ1 − μ2) = 0. Yes, both intervals contain (μ1 − μ2) = 0.No, neither interval contains (μ1 − μ2) = 0.
Why is this of interest to the researcher?
If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0.If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that there is no difference in the average room rates for the two hotels. If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that there was an error in the database records.If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.
(d) Do the data indicate a difference in the average room rates
between the Hotel A and the Hotel C chains?
Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel C chains.
Do the data indicate a difference in the average room rates between
the Hotel B and the Hotel C chains?
Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains.
In: Math
The accompanying data table lists the magnitudes of 50
earthquakes measured on the Richter scale. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00.
0.720, 0,740, 0.640, .390, .700, 2.200, 1.980, .640, 1.220, .200, 1.640, 1.320, 2.950, .900, 1.760, 1.010, 1.260, 0.000, .650, 1.460, 1.620, 1.830, .990, 1.560, .390, 1.280, .830, 1.350, .540, 1.250, .920, 1.000, .780, .790, 1.440, 1.000, 2.240, 2.500, 1.790, 1.250, 1.490, .840, 1.000, 1.250, 1.420, 1.350, .930, .400, 1.390
Use a 0.01 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion for the test. Assume this is a simple random sample.
a. Identify the test statistic. (Round to two decimal places as needed.)
b. Identify the P-value. (Round to three decimal places as needed.)
In: Math
Match the confidence level with the confidence interval for μ. _______ _____ 1. x̄ ± 2.575( σ ) √? _____ 2. x̄ ± 1.96( σ ) √? _____ 3. x̄ ± 1.645( σ ) √? A. 90% B. 95% C. 99%
In: Math
What is the business value of Analytics? Discuss using examples outlined in the article "Competing of Analytics"
In: Math
Develop a C-code to calculate average, median and standard deviation, using 5 numbers as data you input from the keyboard from calculations and compare program output with the hand calculations shown with formula for average, median & standard deviation..
Use suggested approach below for developing the code (other approaches are also possible):
In main define an array of size = 5,
Read in 5 decimal numbers and print the chosen numbers for input; Store input as a array and work with the array only;
define a pointer pointing to the beginning of an array,
pass the array using pointer to function to function_average to compute ‘average’ that is passed back to main;
pass the array using pointer to function to function_median to compute ‘median’ that is passed back to main;
pass the array using pointer to function_standard_derivation to compute ‘standard deviation’ that is pass bac to main;
print results of the computed ‘average’, ‘median’ and ‘standard deviation’ with words of
‘Average of the input five numbers are’, ‘Median of the input five numbers is’ and ‘Standard Deviation of the input five numbers is”
Create function_average
Create function_median,
Create function_standard_derivation
In: Math
Consider the following hypotheses: |
H0: μ ≥ 150 |
HA: μ < 150 |
A sample of 80 observations results in a sample mean of 144. The population standard deviation is known to be 28. Use Table 1. |
a. |
What is the critical value for the test with α = 0.01 and with α = 0.05? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) |
Critical Value | |
α = 0.01 | |
α = 0.05 | |
b-1. |
Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.) |
Test statistic |
b-2. |
Does the above sample evidence enable us to reject the null hypothesis at α = 0.01? |
|
c. |
Does the above sample evidence enable us to reject the null hypothesis at α = 0.05? |
|
In: Math
A researcher wants to evaluate the effectiveness of cognitive behavior therapy which he thinks will decrease depression scores. Prior to testing, each of n = 10 patients rated their current level of depression on a self-report survey. After attending cognitive behavior therapy for a month, a second rating is recorded. The data are as follows:
Before After
5 2
7 7
10 7
14 10
Do the results indicate a significant difference? Use α = .01. If so, what percent of the decrease is actually due to the therapy?
In: Math
Find the following percentile for the standard normal distribution. Draw a sketch and show the R code:
a. 91st percentile
b. 9th percentile
c. 75th percentile
d. 25th percentile
e. 6th percentile
In: Math
Let us consider a random variable X is the element of U(0, a) so that a has been obtained as a sample from a random variable A which follows a uniform distribution A is the element of U(0, l) with known parameter value l.
Estimates of a based on 1) the method of moments, 2) the method of maximum likelihood and 3) the Bayesian-based methods, respectively in R.
Read a data sample of r.v. X from the file
sample_x.csv. Estimate a from such sample, knowing
that l = 10.
i. Using only the first sample.
ii. Using only the first 5 samples.
iii. Using only the first 10 samples.
iv. Using all the samples.
sample_x.csv contains these numbers, please copy the numbers to excel file to write the estimators in R.
2.70251720663915
4.52533716919839
1.7231448657286
2.75834069244788
2.19003083976203
3.19190171690754
3.87230309952386
3.93239850995383
4.93477988922767
1.64963260015239
5.02497814716251
5.92375606054227
6.54048445225238
5.89274455816184
6.81183471748896
3.20217587502456
4.39968432805757
4.78356387178363
2.09551473182655
4.0451138126402
5.61321793564152
5.56420019695387
6.22983582402031
6.51275224747206
6.75733219590838
Please try at least for some estimators... Thank you :)
In: Math
The Food Marketing Institute shows that 16% of households spend
more than $100 per week on groceries. Assume the population
proportion is p = 0.16 and a sample of 900 households will
be selected from the population. Use z-table.
In: Math
6. There are 16 cleaning sponges in a bin at Walmart. 7 are green and the remaining 9 are blue. Suppose I randomly select 4 sponges. What is the probability that: (Round to 4 (FOUR) decimal places.)
a. All four are green?
b. All four are blue?
c. 2 or 3 are blue?
d. None are green?
e. 3 or fewer are green?
In: Math