Description
Submit an HTML document by the beginning of class.
Exercise
Now that we’re officially equipped with IF-statements, let’s create a more robust and powerful hypothesis test function!
Your task is to write a function hyp_test which performs a one-sample hypothesis test about either a mean or a proportion. Your function should take the following arguments:
-
data – a vector of numeric or factor values (this is the sample of data). This sample can have missing (NA) values in it. If numeric, the function will perform a one-sample t-test for a mean. If factor, the function will perform a one-sample z-test for a proportion. For a z-test, the sample proportion will be the proportion of data in the first factor level.
-
null – a single numeric value (this is the hypothesized value).
-
alpha – a single numeric value (this is the significance level). This should default to 0.05.
-
alternative – a character string specifying the form of the alternative hypothsis (“less”, “greater”, “two-sided”). This should default to “two-sided”.
Value
Your function should ignore any missing values in the data and return a list with the following components:
-
statistic : the value of the z- or t-statistic
-
df : degrees of freedom if appropriate
-
p.value : the p-value for the test
-
conf.int : a confidence interval for the proportion (or mean) appropriate to the specified alpha
-
estimate : the estimated proportion (or mean) based on the data
-
null.value : the specified hypothesized value of the proportion (or mean)
-
alpha : the specified significance level
Display
Besides returning the items listed above, your function should print the following:
-
The null hypothesis
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The value of the test statistic and the p-value
-
The confidence interval for the proportion (or mean)
1
NOTE 1: Your function should perform a check to make sure the null hypothesis value is between 0 and 1 for the one proportion test; otherwise, your function should return an error.
NOTE 2: You may NOT use R’s t.test() except to check your work.
Example
Test your code in AT LEAST the following 5 ways.
#TEST 1
data <- c(NA, 5:25)
hyp_test(data, null = 16, alpha = .05, alternative = “two-sided”)
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Ho: mu = 16
-
Test Statistic: -0.74 , p-value: 0.4688
-
Confidence Interval: (12.18,17.82)
-
$statistic
-
[1] -0.7385489
##
-
$df
-
[1] 20
-
$p.value
-
[1] 0.4687599
-
$conf.int
-
[1] 12.17559 17.82441
-
$estimate
-
[1] 15
##
-
$null.value
-
[1] 16
##
-
$alpha
-
[1] 0.05
#TEST 2
data <- factor(c(NA, rep(“a”, 60), rep(“b”, 40)))
hyp_test(data, null = .5, alpha = .01, alternative = “greater”)
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Ho: p = 0.5
-
Test Statistic: 2 , p-value: 0.0228
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Confidence Interval: (0.4738,0.7262)
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$statistic
-
[1] 2
##
-
$p.value
-
[1] 0.02275013
2
-
[1] 0.4738107 0.7261893
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$estimate
-
[1] 0.6
##
-
$null.value
-
[1] 0.5
##
-
$alpha
-
[1] 0.01
-
TEST 3
data <- factor(c(NA, rep(“a”, 60), rep(“b”, 40)))
hyp_test(data, null = 1.4, alpha = .01, alternative = “greater”)
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Error: invalid hypothesized value. Must be between 0 and 1
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[1] NA
-
TEST 4
data <- 1:10
hyp_test(data, null = 6, alpha = .101, alternative = “greater”)
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Ho: mu = 6
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Test Statistic: -0.52 , p-value: 0.6929
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Confidence Interval: (3.75,7.25)
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$statistic
-
[1] -0.522233
##
-
$df
-
[1] 9
-
$p.value
-
[1] 0.6929414
-
$conf.int
-
[1] 3.750928 7.249072
-
$estimate
-
[1] 5.5
##
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$null.value
-
[1] 6
##
-
$alpha
-
[1] 0.101
-
TEST 5
data <- factor(c(NA, rep(“a”, 60), rep(“b”, 40)))
hyp_test(data, null = 0.70, alpha = .02, alternative = “less”)
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Ho: p = 0.7
-
Test Statistic: -2.18 , p-value: 0.0145
3
-
$statistic
-
[1] -2.182179
##
-
$p.value
-
[1] 0.01454817
-
$conf.int
-
[1] 0.4860327 0.7139673
-
$estimate
-
[1] 0.6
##
-
$null.value
-
[1] 0.7
##
-
$alpha
-
[1] 0.02
4
