Question

In: Statistics and Probability

For the question below, state what your null and alternative hypotheses are and select the appropriate...

For the question below, state what your null and alternative hypotheses are and select the appropriate test. Assess assumptions and do whatever needs to be done depending on your results (ie, doing a transformation of data or selecting a non-parametric if data violate assumptions). If you decide to run a Kruskal-Wallis test, you can assume the data satisfy those assumptions. Recall that it is generally considered ok to violate one assumption, especially if sample size is not too small. Perform the test and report the p value with the biological interpretation of your data. Finally, make a plot of the data that DOES NOT have a title, but does have proper x and y axis labels (can do it in excel or SPSS).

1)

You are interested in the connection between vitamin C and bone health. You expose guinea pigs to three different doses of vitamin C and then you record tooth growth following the doses. You collect the following data which are measures of tooth length in mm.

Dose 0.5

Dose 1.0

Dose 2.0

4.2

16.5

23.6

11.5

16.5

18.5

7.3

15.2

33.9

5.8

17.3

25.5

6.4

22.5

26.4

10

17.3

32.5

11.2

13.6

26.7

11.2

14.5

21.5

5.2

18.8

23.3

7

15.5

29.5

Solutions

Expert Solution

For the question below, state what your null and alternative hypotheses are and select the appropriate test. Assess assumptions and do whatever needs to be done depending on your results (ie, doing a transformation of data or selecting a non-parametric if data violate assumptions). If you decide to run a Kruskal-Wallis test, you can assume the data satisfy those assumptions. Recall that it is generally considered ok to violate one assumption, especially if sample size is not too small. Perform the test and report the p value with the biological interpretation of your data. Finally, make a plot of the data that DOES NOT have a title, but does have proper x and y axis labels (can do it in excel or SPSS).

Test for assumptions.

Test for normality shows that Kolmogorov-Smirnov test p values for the 3 groups are 0.20 which is > 0.05 level of significance. This shows that the normality assumption is not violated.

Tests of Normality

Group

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

Tooth length

Dose 0.5

.198

10

.200*

.890

10

.170

Dose 1.0

.217

10

.200*

.908

10

.270

Dose 2.0

.154

10

.200*

.973

10

.919

*. This is a lower bound of the true significance.

a. Lilliefors Significance Correction

1)

You are interested in the connection between vitamin C and bone health. You expose guinea pigs to three different doses of vitamin C and then you record tooth growth following the doses. You collect the following data which are measures of tooth length in mm.

ANOVA used to compare the means of the three groups.

Descriptives

Tooth length

N

Mean

Std. Deviation

Std. Error

95% Confidence Interval for Mean

Minimum

Maximum

Lower Bound

Upper Bound

Dose 0.5

10

7.9800

2.74663

.86856

6.0152

9.9448

4.20

11.50

Dose 1.0

10

16.7700

2.51531

.79541

14.9707

18.5693

13.60

22.50

Dose 2.0

10

26.1400

4.79773

1.51718

22.7079

29.5721

18.50

33.90

Total

30

16.9633

8.26603

1.50916

13.8767

20.0499

4.20

33.90

ANOVA

Tooth length

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

1649.489

2

824.744

67.072

.000

Within Groups

332.001

27

12.296

Total

1981.490

29

Calculated F(2,27) = 67.072, P=0.000 which is < 0.05 level of significance. Ho is rejected. We conclude that three group means are different. We conclude that there is a connection between vitamin C and bone health.



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