Question

Statistics Question please only take if you can answer A company has developed a new kind of antibiotic that they expect to kill 90% of harmful bacteria when applied. The antibiotic is applied to a petri dish full of bacteria and after a reasonable amount of time, a random sample of 100 bacteria were examined and it was found that 86% of them were dead.Let's test the hypothesesH0: p = 0.9versusHa: p < 0.9Using the results of the sample, a test statistics of z = -1.33 was calculated, which yielded a p-value of 0.091.Does this show significant evidence that the proportion of bacteria killed is less than 90% ?

Answer 1

For this significant level of 90%

`\begin{gathered} \alpha\text{ = 1 - 90\%} \\ \alpha\text{ = 1 - 0.9} \\ \alpha\text{ = 0.1} \end{gathered}`
`\begin{gathered} H_0\colon\text{ Null hypothesis is rejected } \\ H_1\colon\text{ Alternate hypothesis is accepted } \\ if\text{ it does at the }\alpha\text{ = 0.1 level but not the }\alpha\text{ = 0.05 level} \\ \text{because the yielded p value is less than the }\alpha\text{ level} \end{gathered}`

Hence the correct answer is the Third Option