Answer:
Step-by-step explanation:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H₀: u = 50
H₁: u ≠ 50
Null hypothesis: The production line produce bags of candy has an average of exactly 50 candies per bag.
Alternative hypothesis: The production line produce bags of candy does not have an average of exactly 50 candies per bag.
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1.0
Test Statistic
t = (x - u) / SE
t = - 2.0
DF = n - 1
D.F = 24
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the t statistic having 24 degrees of freedom is less than -2.0 or greater than 2.0.
Thus, the P-value = 0.057
Statistic result
Interpret results. Since the P-value (0.057) is greater than the significance level (0.05), we failed to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the production line produce bags of candy with an average of exactly 50 candies per bag.
