Determine the Best Fit Linear Regression Equation Using Technology - Excel
Question
The table shows the age in years and the number of hours slept per day by 24 infants who were less than 1 year old. Use Excel to find the best fit linear regression equation, where age is the explanatory variable. Round the slope and intercept to one decimal place.
Age
Hours
0.03
16.5
0.05
15.2
0.06
16.2
0.08
15.0
0.11
16.0
0.19
16.0
0.21
15.0
0.26
14.5
0.34
14.6
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In: Math
8.3 Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 707 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion? Appendix A Statistical Tables
(Round the intermediate values to 3 decimal places. Round your answer to 3 decimal places.)
___________ ≤ p ≤ __________
The point estimate is _______.
In: Math
Suppose that the height of Australian males is a normally distributed random variable with a mean of 176.8cm and a standard deviation of 9.5cm.
a. If the random variable X is the height of an Australian male, identify the distribution of X and state the value/s of its parameter/s.
b. Calculate (using the appropriate statistical tables) the probability that a randomly selected Australian man is more than two metres tall.
c. To become a jockey, as well as a passion for the sport, you need to be relatively small, generally between 147cm and 168cm tall. Calculate (using the appropriate statistical tables) the proportion of Australian males who fit this height range.
d. Some of the smaller regional planes have small cabins, consequently the ceilings can be quite low. Calculate (using the appropriate statistical tables) the ceiling height of a plane such that at most 2% of the Australian men walking down the aisle will have to duck their heads.
e. Verify your answers to parts b., c. and d. using the appropriate Excel statistical function and demonstrate you have done this by including the Excel formula used.
f. A random sample of forty Australian males is selected. State the type of distribution and the value/s of the parameter/s for the mean of this sample.
g. Calculate (using the appropriate statistical tables) the probability that the average height of this sample is less than 170cm.
In: Math
1)
Assume that a sample is used to estimate a population mean μμ. Find the 99.9% confidence interval for a sample of size 585 with a mean of 74.4 and a standard deviation of 16.6. Enter your answers accurate to four decimal places.
Confidence Interval:
2) You measure 20 textbooks' weights, and find they have a mean
weight of 74 ounces. Assume the population standard deviation is
10.9 ounces. Based on this, construct a 95% confidence interval for
the true population mean textbook weight.
Keep 4 decimal places of accuracy in any calculations you do.
Report your answers to four decimal places.
Confidence Interval:
3)
A population of values has a normal distribution with μ=146.5μ=146.5 and σ=53.4σ=53.4. You intend to draw a random sample of size n=114n=114.
Find the probability that a single randomly selected value is
less than 141.
P(X < 141) =
Find the probability that a sample of size n=114n=114 is
randomly selected with a mean less than 141.
P(¯xx¯ < 141) = Enter your answers as
numbers accurate to 4 decimal places.
4)
CNNBC recently reported that the mean annual cost of auto
insurance is 987 dollars. Assume the standard deviation is 257
dollars. You take a simple random sample of 94 auto insurance
policies.
Find the probability that a single randomly selected value is less
than 968 dollars.
P(X < 968) =
Find the probability that a sample of size n=94n=94 is randomly
selected with a mean less than 968 dollars.
P(¯xx¯ < 968) =
Enter your answers as numbers accurate to 4 decimal places.
In: Math
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 18 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.30 gram.
(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)
| lower limit | |
| upper limit | |
| margin of error |
(b) What conditions are necessary for your calculations? (Select
all that apply.)
uniform distribution of weightsσ is unknownσ is knownn is largenormal distribution of weights
(c) Interpret your results in the context of this problem.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean. There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
(d) Find the sample size necessary for an 80% confidence level with
a maximal margin of error E = 0.12 for the mean weights of
the hummingbirds. (Round up to the nearest whole number.)
hummingbirds
In: Math
For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
A random sample of 5400 permanent dwellings on an entire
reservation showed that 1648 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
answer to three decimal places.)
| lower limit | |
| upper limit |
Give a brief interpretation of the confidence interval.
99% of all confidence intervals would include the true proportion of traditional hogans.
1% of all confidence intervals would include the true proportion of traditional hogans.
99% of the confidence intervals created using this method would include the true proportion of traditional hogans.
1% of the confidence intervals created using this method would include the true proportion of traditional hogans.
(c) Do you think that np > 5 and nq > 5 are
satisfied for this problem? Explain why this would be an important
consideration.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.
In: Math
A courier service advertises that its average delivery time is less than 6 hours for local deliveries. A sample of 16 local deliveries was recorded and yielded the statistics x = 5.83 hours and s = 1.59 hours. At the 5% significance level, conduct a hypothesis test to determine whether there is sufficient evidence to support the courier’s advertisement.
In: Math
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 65 and 67 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of twenty-three 18-year-old men is selected,
what is the probability that the mean height x is between
65 and 67 inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is the probability
in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability in part (b) is much higher because the mean is larger for the x distribution.
In: Math
Store Customers (X) Average Profits (Y)
A 161 157
B 99 93
C 135 136
D 120 123
E 164 153
F 221 241
G 179 201
H 204 206
I 214 229
J 101 135
K 231 224
L 206 195
M 248 242
N 107 115
O 205 197
Use the Spearman’s Rank Correlation test at the 0.05 level to see if X and Y are significantly related.
In: Math
Design A Design B Design C
16 33 23
18 31 27
19 37 21
17 29 28
13 34 25
Use the Kruskal-Wallis H test and the Chi-Square table at the 0.05 level to compare the three designs.
In: Math
The following are quality control data for a manufacturing process at Kensprt Chemical Company. The data show the temperature in degrees centigrade at five points in time during the manufacturing cycle. The company is interested in using quality control charts in monitoring the temperature of its manufacturing cycle. Construct an X bar and R chart and indicate what its tells you about the process.
Sample X bar R
1 95.72 1.0
2 95.24 .9
3 95.38 .8
4 95.44 .4
5 95.46 .5
6 95.38 1.1
7 95.40 .9
8 95.44 .3
9 95.08 .2
10 95.50 .6
11 95.80 .6
12 95.22 .2
13 95.56 1.3
14 95.22 .5
15 95.74 .8
16 95.72 1.1
17 94.82 .6
18 95.46 .5
19 95.60 .4
20 95.64 .6
In: Math
An airline operates a call center to handle customer questions and complaints. the airline monitors a sample of calls to help ensure that the service being offered is of high quality. The random samples of 100 calls each were monitored under normal conditions. The center can be thought of as being in control when these 10 samples were taken. The number of calls in each sample not resulting in a satisfactory resolution for the customer is as follows:
4 5 3 2 3 3 4 6 4 7
a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control?
b. Construct the upper and lower limits for a p chart for the process.
c. With the results in part b. what is your conclusion if a sample of 100 calls has 12 calls not resulting in a satisfactory outcome for the customer?
In: Math
A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 10 nursing students from Group 1 resulted in a mean score of 65.8 with a standard deviation of 5.1. A random sample of 16 nursing students from Group 2 resulted in a mean score of 70.4 with a standard deviation of 7.6. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
Step 1 of 4: State the null and alternative hypotheses for the test.
Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
Step 4 of 4: State the test's conclusion.
In: Math
Observed
Frequency
Brand of Preferences
A 102
B 121
C 120
D 57
Use an Excel spreadsheet to test this hypothesis at the 0.05 level. Submit the Excel spreadsheet you create along with an explanation of results
In: Math
A certain drug is tested for its effect on blood pressure. Seven male patients have their systolic blood pressure measured before and after receiving the drug with the results shown below (in mm Hg).
Patient SBP before SBP after
1 120 125
2 124 126
3 130 138
4 118 117
5 140 143
6 128 128
7 140 146
a. (2) State, in prose, the study hypothesis (two-tailed).
b. (2) What test statistic(s) test would you use?
c. (2) What is the critical value of the test statistic?
d. (3) If the value of the test statistic is t = 2.67, what do you conclude (reject/do not reject is not sufficient).
In: Math