Hypothesis testing is a statistical method for testing a claim or hypothesis about a population parameter. It is an important tool in statistical inference and helps us to make decisions based on data.

The basic steps involved in hypothesis testing are:

1. Stating the null and alternative hypotheses
2. Selecting a test statistic
3. Calculating the p-value
4. Making a conclusion

The chickwts dataset in R shows weight of chickens at different ages and will be used for plotting and hypothesis testing. This boxplot shows the distribution of chick weights by type of feed, with the x-axis showing the type of feed and the y-axis showing the weight of the chicks in grams

This plot shows the distribution of chick weights in the chickwts dataset. The x-axis displays weight and the y-axis displays frequency. The plot is a histogram with 20 bins and is filled in gray with a black border.

The null hypothesis is a statement of no effect or no difference, while the alternative hypothesis is the opposite of the null hypothesis. In hypothesis testing, we compare the observed data to what we would expect to see if the null hypothesis were true.

For this dataset, we can formulate the null and alternative hypotheses as follows:

\[H_0: \mu = \mu_0\] \[ H_A: \mu \neq \mu_0 \]

H0: The mean weight of chickens is equal to 500 g

Ha: The mean weight of chickens is not equal to 500 g

The t-test splits the weight data into two groups and calculates the difference between their means divided by the standard error.

The p-value is the probability of observing a test statistic as extreme or more extreme than the one observed, under the assumption that the null hypothesis is true.

\[ p = P(X \geq x) \]

options(scipen = 999)
result <- t.test(weight ~ group, data = chickwts)
p.value <- result$p.value
p.value

## [1] 0.0000000000000000001530996

A p-value less than .05 indicates STRONG evidence AGAINST the null hypothesis and supports the alternative hypothesis. A p-value greater than .05 indicates WEAK evidence AGAINST the null hypothesis and FAILS to support to the alternative hypothesis.

if (p.value < 0.05) {
  print("Reject the null hypothesis")
} else {
  print("Fail to reject the null hypothesis")
}

## [1] "Reject the null hypothesis"

• Hypothesis testing performed on chick weight data
• Null hypothesis: mean weight of all chicks is equal to a specified value
• Alternative hypothesis: mean weight of all chicks is not equal to the specified value
• Used a t-test to calculate p-value
• p-value indicates evidence against the null hypothesis, suggesting that the mean weight of all chicks is not equal to the specified value.