Will associative property work for 4(m+3+5m)? if so show how it will look like after you use associative property

Because the P-value of 0.0733 > Alpha, Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Step-by-step explanation:

To understand this question, you'll have to understand a few terms: the null hypothesis, the alternative hypothesis, the p-value and the signifiance level.

The null hypothesis (H₀) is the assumption that the phenomenon doesn't exist - in this case, it is that the proportion of customers who will ask for a straw is 50%, or due to chance (you can either ask for a straw or not). When doing a statistical test for the existance of a phenomenon, we usually assume the null hypothesis to be true first.

The alternative hypothesis (Hₐ) is the assumption that a phenomenon is true. In this case, it is that that the proportion of customers who will ask for a straw is less than 50%.

The p-value is usually a result you get after performing the statistical test - it's the probability that the observed results are at least as extreme as the results actually observed, assuming that the null hypothesis is true. In this case, assuming that the proportion of customers who will ask for a straw is 50% (the null hypothesis), a p-value of 0.0733 for the observed result of 43 customers means that if the experiment were to be repeated again, then there is a 7.33% chance that 43 customers or less will ask for a straw, assuming the null hypothesis is true. This seems pretty good - assuming the null hypothesis is true, there's only a 7.33% chance that we could have gotten 43 customers or less, which means it may be reasonable to "reject the null hypothesis" (i.e. the alternative hypothesis may be true).

However, in many cases a 7.33% chance may not be low enough, e.g. in this problem, a less than 5% chance (i.e. p < 0.05) is necessary. This required chance for results to be statistically significantly is called the signifiance level, or alpha value, the "the probability of rejecting the null hypothesis when the null hypothesis is in fact true." In scientific journals or depending on the field of study, there may be a generally accepted signifiance level.