Question

In: Statistics and Probability

(10 marks) A medical researcher is interested in whether calcium intake differs, on average, among elderly...

A medical researcher is interested in whether calcium intake differs, on average, among elderly individuals with normal bone density, with osteopenia (a low bone density that may lead to osteoporosis), and with osteoporosis. He recruits consenting 60 individuals over the age of 65 using his patient records from his hospital (20 from each of the three bone density groups). You may assume that the individuals in each group constitute a simple random sample from consenting patients from that hospital. The individuals keep a food diary for two weeks, at the end of which the researcher computes their average daily calcium intake (in mg). The data are available in the file calcium.csv.

CALCIUM.CSV:

   calcium        group
1      861       normal
2      884       normal
3     1009       normal
4      905       normal
5      909       normal
6     1020       normal
7      932       normal
8      811       normal
9      852       normal
10     869       normal
11     986       normal
12     925       normal
13     928       normal
14     908       normal
15     861       normal
16    1025       normal
17     935       normal
18     762       normal
19     949       normal
20     867       normal
21     675   osteopenia
22     735   osteopenia
23     678   osteopenia
24     699   osteopenia
25     706   osteopenia
26     632   osteopenia
27     809   osteopenia
28     761   osteopenia
29     670   osteopenia
30     838   osteopenia
31     780   osteopenia
32     729   osteopenia
33     813   osteopenia
34     811   osteopenia
35     808   osteopenia
36     798   osteopenia
37     789   osteopenia
38     746   osteopenia
39     729   osteopenia
40     723   osteopenia
41     651 osteoporosis
42     685 osteoporosis
43     611 osteoporosis
44     852 osteoporosis
45     785 osteoporosis
46     621 osteoporosis
47     672 osteoporosis
48     667 osteoporosis
49     755 osteoporosis
50     694 osteoporosis
51     718 osteoporosis
52     698 osteoporosis
53     697 osteoporosis
54     796 osteoporosis
55     684 osteoporosis
56     806 osteoporosis
57     592 osteoporosis
58     741 osteoporosis
59     709 osteoporosis
60     715 osteoporosis

a. What are the null and alternative hypotheses?

b. (1 mark) What is the value of the test statistic?

c. (1 mark) What is the p-value?

d. Using a significance level of α = 0.05, state your conclusions in the language of the problem.

e. State and verify (using plots and/or descriptive statistics) the additional two assumptions required for the p-value in c) to be valid.

Solutions

Expert Solution

here we use F-test using one-way anova

(a) Null hypothesis H0:normal=osteopenia=osteoporosis

alternate hypothesis Ha: atleast one is different from others

(b) F=55.211 ( the F-value of between group )

(c) p-value=0.000 (4.61E-14)

(d) Since p-value is less than typical alpha=0.05, so we reject the null hypothesis and conclude that Yes, calcium intake differs, on average, among elderly individuals with normal bone density, with osteopenia (a low bone density that may lead to osteoporosis), and with osteoporosis.

 
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 20 18198 909.9 4641.463
Column 2 20 14929 746.45 3389.208
Column 3 20 14149 707.45 4507.208
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 461486 2 230743 55.21102 4.61E-14 3.158843
Within Groups 238219.7 57 4179.293
Total 699705.7 59

Related Solutions

A medical researcher is interested in whether calcium intake differs, on average, among elderly individuals with...
A medical researcher is interested in whether calcium intake differs, on average, among elderly individuals with normal bone density, with osteopenia (a low bone density that may lead to osteoporosis), and with osteoporosis. He recruits consenting 60 individuals over the age of 65 using his patient records from his hospital (20 from each of the three bone density groups). You may assume that the individuals in each group constitute a simple random sample from consenting patients from that hospital. The...
Hypothesis testing using Z statistics: A researcher is interested in whether short-term memory in the elderly...
Hypothesis testing using Z statistics: A researcher is interested in whether short-term memory in the elderly is different from short-term memory in the general population. The literature suggests that short-term memory declines with age. Population mean=125                  Sample mean=121 Population SD=10                         Sample size=36 Test the hypothesis that the elderly sample has significantly less short-term memory than the general population. Use α = .05 State your z-statistic in appropriate APA format. What is your decision? Do you need to calculate a Cohen’s...
[6 marks] A researcher was interested in finding out whether Moral Reasoning could be enhanced if...
[6 marks] A researcher was interested in finding out whether Moral Reasoning could be enhanced if students were taught using Moral Dilemmas. Subjects were given a Moral Reasoning Test before the treatment (using moral dilemmas) and after the treatment and the results are shown in Table 1 below. Table 1 : Mean Moral Reasoning Score Before and After Teaching Using Moral Dilemmas N Mean Std. Deviation Std. Error Mean Pretest 30 18.50 5.33 0.97 Posttest 30 23.86 4.75 0.87 Describe...
a) A researcher is interested in determining if the IQ’s of prison inmates differs from the...
a) A researcher is interested in determining if the IQ’s of prison inmates differs from the that the general population, which has been shown to have a mean IQ of 100 and a standard deviation of 15. The researcher recruits a random sample of 25 inmates and finds that the average IQ is 105.3 points. Test the null hypothesis at the .05 level. Show all work and present a step by step hypothesis test summary as shown in the text....
A researcher is interested in studying average hours per year spent on continuous medical education by...
A researcher is interested in studying average hours per year spent on continuous medical education by physicians in a large hospital system. The data is limited to demographics (age, race, gender), professional characteristics (years worked in the field, specialty) and self-reported hours of CME. What is the independent variable? What is the dependent variable? Is the dependent variable continuous or categorical? Is the independent variable(s) continuous or categorical?
A researcher is interested in the effects of sleep deprivation and caffeine intake on mood. Participants...
A researcher is interested in the effects of sleep deprivation and caffeine intake on mood. Participants were randomly assigned to a sleep condition (normal or deprived) and a caffeine condition (0 cups, 2 cups, or 4 cups). After the manipulations, mood was measured (such that higher numbers indicated better mood). The results were as follows:                    Normal Condition                                      Deprived Condition          0 cups        2 cups        4 cups                    0 cups        2 cups        4 cups             16              18              18                          0               ...
Mechanism of Hypothalamus Regulate Food Intake (10 marks)
Mechanism of Hypothalamus Regulate Food Intake
A) A researcher is interested in knowing the level of job satisfaction among employees in a...
A) A researcher is interested in knowing the level of job satisfaction among employees in a large company. He measures job satisfaction on a 5-point scale where 1=” Extremely dissatisfied” and 5 = “Extremely satisfied”. What is the matching description of the variable of interest in this study? Group of answer choices a. Quantitative / Discrete b. Quantitative / Continuous c. Categorical / Ordinal d. Categorical / Nominal B) What is the most suitable measure of centre for a skewed...
A researcher is interested in whether or not there is a difference in student’s performance based...
A researcher is interested in whether or not there is a difference in student’s performance based on the study methods they use. Participants are assigned one of three different study methods (read the text and re-read it, read and answer prepared questions, and read then create your own questions). There are 6 people in each group and the researcher measures the participants’ performance on a test. Perform a hypothesis test and show all four steps. Hints: Use a two tailed...
In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in...
In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in gender differences as related to binge drinking and to drinking-related arrests. She wanted to know two things: (a) Is there a significant relationship between gender and binge drinking (as defined by 5 or more drinks at one sitting), and (b) Is there a significant relationship between gender and drinking-related arrests? A random sample of males and females were asked about their experiences with binge...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT