1. State a null and working/alternative hypothesis for this problem SLOPE ANGLE
ID: 3053166 • Letter: 1
Question
1. State a null and working/alternative hypothesis for this problem SLOPE ANGLE BY SUBSTRATE (in degrees from horizontal) Limestone 32.1 29.4 33.0 27.3 19.0 14.4 21.1 25.5 Clastic Sedimentary 17.8 15.8 12.5 15.5 15.1 12.2 13.1 10.6 9.3 5.5 10.5 10.5 11.0 14.2 a) Considering that you don't have population variances for slope angles in each substrate type and that you have only 13 and 10 transects for limestone and clastic sedimentary substrates, respectively, which test should you use, Z test or t test? b) Given the form of your null hypothesis, are you about to do a one-tail or two-tail test? Calculate the mean, standard deviation, and variance for both the limestone and the clastic sedimentary slopes. Place these into a summary table for reference. d) Now, eyeballing the standard deviations above, are they similar enough to warrant a pooled estimate of the population variance (PVE), or should you use the separate variance estimate (SVE)? Why? (A good rule of thumb is that a pooled estimate can be used where the variances differ by less than a factor of two.) e) Having made your decision about the PVE or SVE choice, calculate the 2-sample test statistic for the difference of means. (Zo f) Now, using the right table the right way, what is the critical statistic (text or Zt) for your samples? g) On thebasis.of the comparison between the observed and the critical statistic, will you accept or reject the null hypothesis? h) Briefly interpret your findings in clear English.Explanation / Answer
Here we have given that two groups are lime stone and clastic sedimentary each of size 13 and 10 respectively.
1) Here we have to test the hypothesis that,
H0 : Two population means are equal.
H1 : Two population means are differ.
Assume alpha = level of significance = 0.05
a) Here sample sizes are less than 30 and population variances are unknown so we use two sample t-test.
b) This is two tailed test since alternative hypothesis contains not equal to sign.
c) Now we have to find mean, variance and standard deviation for both the variables.
This we can find in excel.
steps :
ENTER data into excel sheet --> Data --> Data analysis --> Descriptive statistics --> ok --> Input range: Select data columns --> Grouped by : columns --> Click on labels in first row --> Output range : select one empty cell --> summary statistics --> ok
d) Here we have to first test whether variances are equal or not.
Hypothesis for the test is,
H0 : Variances are equal.
H1 : Variances are not equal.
The test statistic follows F-distribution.
The test statistic is,
F = largest variance / smallest variance
This also we can test in excel.
steps :
ENTER data into excel sheet --> Data --> Data analysis --> F-Test two sample for variances --> ok --> Variable 1 Range : select limestone data --> Variable 2 Range : Select clastic sedimentary data --> Labels --> Alpha : 0.05 --> Output range : select one empty cell --> ok
Test statistic = 5.96
P-value = 0.0058
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : Variances are not equal.
Therefore we can't use here pooled estimate.
e) Test statistic is,
T = (X1bar - X2bar) / sqrt [s12 / n1 + s22 / n2 ]
We can do this test in excel.
steps :
ENTER data into excel sheet --> Data --> Data analysis --> t-test : Two sample assuming unequal variances --> ok --> Variable 1 Range : select limestone data --> variable 2 Range : select clastic sedimentary data --> Hypothesized mean difference : 0 --> Click on labels --> Alpha : 0.05 --> Output Range : select one empty cell --> ok
Output :
Test statistic = 2.61
f) P-value = 0.0185
P-value < alpha
g) Reject H0 at 5% level of significance.
h) Conclusion : Two population means differ.
We get significant result about t-test.
mean variance standard deviation 19.78 77.85 8.82 12.74 13.05 3.61Related Questions
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