8. A brand of penne pasta contains an average of 354 individual penne per box. Subash thinks there are
more penne per box than what is being reported. He buys a random sample of boxes from several
dierent stores and calculates a sample mean of 357. Write null and alternative hypotheses to describe
this situation.
Null hypothesis (H0): The true population mean of individual penne per box is equal to 354.
Alternative hypothesis (Ha): The true population mean of individual penne per box is greater than 354.
Null hypothesis (H0): The average number of individual penne per box is equal to 354.
Alternative hypothesis (H1): The average number of individual penne per box is greater than 354.
To write the null and alternative hypotheses for this situation, we need to understand the claim Subash is making and what he wants to test.
In this case, Subash thinks that there are MORE penne per box than what is being reported (i.e., the reported average of 354). So, we can say that Subash's claim is that the true average number of penne per box is greater than 354.
Based on this claim, we can write the null and alternative hypotheses as follows:
Null Hypothesis (H0): The true average number of penne per box is equal to or less than 354.
Alternative Hypothesis (Ha): The true average number of penne per box is greater than 354.
Symbolically, it can be represented as:
H0: μ <= 354 (where μ represents the true population mean)
Ha: μ > 354
These hypotheses will be used to test Subash's claim and determine if there is enough evidence to support the alternative hypothesis.