Question

A grocery store manager claims that 75% of shoppers purchase bananas at least once a month. Technology was used to simulate choosing 150 SRSs of size n = 100 from a population of shoppers where 75% buy bananas. The dot plot shows p = the sample proportion of shoppers who bought bananas in the past month. A random sample of 100 shoppers from the store were selected and 64 bought bananas in the past month. Does this sample provide evidence that the grocery store manager overstated the true proportion? Justify your answer.

Answer 1

Step-by-step explanation:

The goal here is to test whether the population proportion (p) is overstated i.e if it is actually less.

The null hypothesis & alternative hypothesis is:

`\mathbf{H_o: p = 0.75}`

`\mathbf{H_a: p < 0.75}`

The sample proportion
`\hat p = (64)/(100)`

`\hat p = 0.64\\`

From the dot plot, we are to determine the p-value for this test i.e
`P(\hat p < 0.64)`

However, the number of times
`\hat p < 0.64` in 150 simulations = 5

∴

`P(\hat p < 0.64) = (5)/(150)= 0.0333`

p-value = 0.033 < 0.05 < ∝

Hence, we reject the
`\mathbf{H_o}` at 5% significance level and conclude that the proportion of shoppers who bought bananas at least once in the past month is oversrtated.