How do I do these computations without a normal distribution chart and just a TI84 calculator?
6.7 Given a standard normal distribution, ﬁnd the value of k such that
(a) P(Z>k)=0 .2946;
(b) P(Z<k)=0 .0427;
(c) P(−0.93 <Z<k)=0 .7235.
6.8 Given a normal distribution with μ = 30 and σ = 6, ﬁnd
(a) the normal curve area to the right of x = 17;
(b) the normal curve area to the left of x = 22;
(c) the normal curve area between x = 32 and x = 41;
(d) the value of x that has 80% of the normal curve area to the left;
(e) the two values of x that contain the middle 75% of the normal curve area.
In: Math
A person’s muscle mass is expected to be associated with age. Some people also thought exercise time would be associated with the muscle mass. To explore the potential relationships between muscle mass and age, muscle mass and exercise time, a nutritionist randomly selected 20 women from a population of women with age ranging from 40 to 80 years old, and measured their muscle mass (a score without unit) and exercise time (hours per month)
Patient |
Age |
MuscleMass |
ExcerciseTime |
1 |
43 |
106 |
23 |
2 |
41 |
106 |
24 |
3 |
47 |
97 |
26 |
4 |
76 |
56 |
21 |
5 |
72 |
70 |
23 |
6 |
76 |
74 |
19 |
7 |
42 |
105 |
22 |
8 |
49 |
97 |
17 |
9 |
53 |
92 |
14 |
10 |
44 |
103 |
21 |
11 |
63 |
80 |
25 |
12 |
55 |
90 |
16 |
13 |
66 |
77 |
25 |
14 |
58 |
86 |
19 |
15 |
70 |
72 |
18 |
16 |
57 |
87 |
22 |
17 |
71 |
71 |
21 |
18 |
46 |
100 |
18 |
19 |
61 |
83 |
27 |
20 |
68 |
74 |
20 |
21 |
44 |
105 |
21 |
22 |
53 |
94 |
19 |
23 |
60 |
82 |
23 |
24 |
72 |
78 |
21 |
What do the two regression parameters (b0 and b1) mean?
In: Math
1)Your master's dissertation concerns recent immigrants' experiences of severe financial strain. A large sample of 960 residents of a medium-sized city indicated that 80% of new immigrants felt that they were extremely stressed financially (which was higher than what is average for the general population). If you were to construct a 99% confidence interval for your finding, what would be the LOWER LIMIT of the interval? (Write as a proportion to 3 decimal places, rather than a percentage)
2) This question is similar to EOC 7.34. Your master's dissertation concerns recent immigrants' experiences of severe financial strain. A large sample of 960 residents of a medium-sized city indicated that 80% of new immigrants felt that they were extremely stressed financially (which was higher than what is average for the general population.) If you were to construct a 99% confidence interval for your finding, what would be the UPPER LIMIT of the interval (written as a proportion to 3 decimal places, rather than a percentage)?
In: Math
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 9 phones from the manufacturer had a mean range of 1180 feet with a standard deviation of 35 feet. A sample of 15 similar phones from its competitor had a mean range of 1120 feet with a standard deviation of 20 feet. Do the results support the manufacturer's claim? Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
Step 2 of 4 : Compute the value of the t test statistic. Round your answer to three decimal places.
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
Calculate the average value of the numbers 3, 3, 5, 5 first by calculating the normal average and then by calculating the weighted average. Are the two results the same?
In: Math
Populations may be _____________ or ________________________. A real population is one in which all observations are ______________________________ at the time of sampling. A hypothetical population is one in which all observations are _____________________________ at the time of ___________________. Often it is not convenient or even possible to include all observations in a research project. In such cases, a _____________________ or subset of observations is taken. The size of the sample is partially determined by estimated ___________________________among observations and by an acceptable amount of _______________________. In order to use inferential statistics, the analysis must be based on a ____________________ sample. A sample is random, if at each stage of the sampling, the selection process guarantees that all remaining __________________ have ____________________ chances of being selected. The observations in a randomly selected sample should be ___________________ of those in the population. However, there is no guarantee of this. The term random describes the process, and not necessarily the outcome. One of the best-known techniques for selecting a random sample is the ________________ method. All observations must be represented on slips of paper that are deposited in a bowl and _________________. The through stirring is a very important aspect of this method of sample selection. Another method for generating a random sample involves the use of the table of ____________ numbers. When using this table, the number of digits actually used is determined by the ____________ __________________. This method is not very efficient for obtaining a sample from a ____________ population. In an experiment, although subjects may not be selected randomly, they should be randomly assigned to either the experimental or control condition. The purpose of random assignment is to make sure that, except for __________________ differences, groups of subjects are similar with respect to any ____________________________________________. It is usually desirable that _____________ numbers of subjects be assigned to the experimental and control groups. To accomplish this, assignment should be done in ______________________.
In: Math
In: Math
A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.
Language | |||
Spanish | French | German | |
System 1 | 6 | 11 | 10 |
10 | 15 | 14 | |
System 2 | 5 | 18 | 14 |
9 | 20 | 20 |
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use = .05.
Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |
Factor A | |||||
Factor B | |||||
Interaction | |||||
Error | |||||
Total |
In: Math
Using the simple random sample of weights of women from a data set, we obtain these sample statistics: n equals = 35 and x =146.25 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by sigma σ equals = 30.78 lb. a. Find the best point estimate of the mean weight of all women. b. Find a 95% confidence interval estimate of the mean weight of all women.
In: Math
Let A, B, and C be independent random variables, uniformly distributed over [0,6],[0,11], and [0,2] respectively. What is the probability that both roots of the equation Ax^2+Bx+C=0 are real?
In: Math
Someone claims that the mean number of sick days that employees in New Jersey take per year is 5.3. To look into that claim, you take a representative sample of 78 employees in New Jersey and find that the mean number of sick days is 5.5 in the sample. The population standard deviation is 1.6.
Part (a)
Given that the sample mean is different from the claimed population mean, does that show that the claim in H_{0} is false? Explain your answer.
Part (b)
Carry out a hypothesis test for the claim above (with α = 0.05) using the 6-step procedure.
Part (c)
Carry out a hypothesis test for the claim above (with α = 0.05) using the p-value method.
In: Math
Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.
Time | A | B | C | F | Row Total |
1 h | 24 | 43 | 61 | 10 | 138 |
Unlimited | 16 | 45 | 83 | 18 | 162 |
Column Total | 40 | 88 | 144 | 28 | 300 |
(i) Give the value of the level of significance.
State the null and alternate hypotheses.
H_{0}: Time to take a test and test score are
not independent.
H_{1}: Time to take a test and test score are
independent. H_{0}: The distributions for a timed
test and an unlimited test are the same.
H_{1}: The distributions for a timed test and an
unlimited test are different.
H_{0}: The distributions for a timed test and an
unlimited test are different.
H_{1}: The distributions for a timed test and an
unlimited test are the same. H_{0}: Time to take a
test and test score are independent.
H_{1}: Time to take a test and test score are not
independent.
(ii) Find the sample test statistic. (Round your answer to two
decimal places.)
(iii) Find or estimate the P-value of the sample test
statistic.
P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005
(iv) Conclude the test.
Since the P-value < α, we reject the null hypothesis. Since the P-value is ≥ α, we do not reject the null hypothesis. Since the P-value < α, we do not reject the null hypothesis. Since the P-value ≥ α, we reject the null hypothesis.
(v) Interpret the conclusion in the context of the application.
At the 1% level of significance, there is insufficient evidence to claim that time to do a test and test results are not independent. At the 1% level of significance, there is sufficient evidence to claim that time to do a test and test results are not independent.
In: Math
In: Math
"A random survey of 927 adults in California found that 63% of them say they are likely to sleep when they stay home sick."
e. Construct a 95% confidence interval for p. (Be sure to follow the whole process).
f. Is it plausible to say that 70% of all California adults would sleep when they stay home sick?
g. Perform a hypothesis test to determine if more than 60% of adults would sleep when they stay home sick.
h. If we made an error here, then would it be a Type I or a Type II error?
In: Math
The director of a Masters of Public Administration Program is preparing a brochure to promote the
program. She would like to include in the brochure the average grade point average (GPA) of first-
year students in the program, but since time is pressing she decides to estimate this figure with a
sample of ten students (GPAs are normally distributed). The GPAs are listed below. What is the best
estimate of the average GPA for all first-year students? With 95% confidence, can the director
conclude the average GPAs for first-year students is a B or better (3.0 on a 4.0 scale)?
2.8
3.6
3.4
2.5
2.2
2.6
4.0
3.1
2.7
3.5
In: Math