ere are the answers to your questions:
The tail category of the hypothesis test is left-tailed. This is because the alternative hypothesis, H
a
, states that the population mean is less than 20.
The implication of the p-value is that the probability of obtaining a sample mean of 18 or less, if the population mean is actually 20, is 0.023. This means that the evidence is significant at the 5% level.
The conclusion is that we reject the null hypothesis. This means that there is sufficient evidence to support the alternative hypothesis, which states that the population mean is less than 20.
Here is a more detailed explanation of the hypothesis test:
The null hypothesis, H
0
, states that the population mean is equal to 20.
The alternative hypothesis, H
a
, states that the population mean is less than 20.
The test statistic is calculated as follows: t = (sample mean - hypothesized mean) / (standard error of the mean)
In this case, the test statistic is equal to -2.23.
The p-value is calculated as follows: p-value = P(t < -2.23)
n this case, the p-value is equal to 0.023.
The decision rule is to reject the null hypothesis if the p-value is less than or equal to the significance level. In this case, the significance level is 0.05.
Since the p-value is less than the significance level, we reject the null hypothesis. This means that there is sufficient evidence to support the alternative hypothesis, which states that the population mean is less than 20.