Two sided or one sided test of hypothesis of mu of one normal sample

Compute the two sided or one sided test of hypothesis of mu of one normal sample when the population variance is known or unknown.

Usage

mean_test1(x, mu = 0, sigma = -1, side = 0)

Arguments

x: A numeric vector.
mu: mu is mu0 in the null hypothesis. Default is 0, i.e., H0: mu = 0.
sigma: The standard deviation of the population. sigma>=0 indicates it is known, sigma<0 indicates it is unknown. Default to unknown standard deviation.
side: A parameter used to control two sided or one sided test of hypothesis. When inputting side = 0 (default), the function computes two sided test of hypothesis, and H1: mu != mu0; when inputting side = -1 (or a number < 0), the function computes one sided test of hypothesis, and H1: mu < mu0; when inputting side = 1 (or a number > 0), the function computes one sided test of hypothesis, and H1: mu > mu0.

Value

A data.frame with variables:

mean: The sample mean.
df: The degree of freedom.
statistic: The statistic, when sigma>=0, statistic = Z = (xb-mu)/(sigma/sqrt(n)); when sigma<0, statistic = T = (xb-mu)/(sd(x)/sqrt(n)).
p_value: The P value.

References

Zhang, Y. Y., Wei, Y. (2013), One and two samples using only an R funtion, doi:10.2991/asshm-13.2013.29 .

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
#>  [1] 1.0753290 1.1944273 1.0517805 1.2414938 0.9461027 0.8603386 0.7023488
#>  [8] 1.4926738 1.1138596 0.7778598
mean_test1(x, mu = 1, sigma = 0.2, side = 1)
#>       mean df         Z   p_value
#> 1 1.045621 10 0.7213377 0.2353509
mean_test1(x, mu = 1)
#>       mean df         T   p_value
#> 1 1.045621  9 0.6122542 0.5555203