Question

1- In a clinical trial, 20 out of 600 patients taking a prescription drug complained of flulike symptoms. Suppose that it is known that 5.5 % of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that less than 5 % of this drug's users experience flulike symptoms as a side effect at the α=0.04 level of significance?

What is the critical value?

2-In a recent survey, 56 % of employed adults reported that basic mathematical skills were critical. A supervisor thinks this percentage has increased due to increased use of technology in the workplace. She takes a random sample of 470 employed adults and finds that 281 of them feel that basic mathematical skills are critical or very important to their job. Test her hypothesis at the α=0.05 level of significance.

What is the critical value?

3-A survey asked, "Do you currently have tattoos on your body?" Of the 1239 males surveyed, 179 responded that they had at least one tattoo. Of the 1057 females surveyed, 141 responded that they had at least one tattoo. Test if the male population proportion is greater in having tattoos at a 95 % confidence level

What is the critical value?

Answer 1

(1) We have to test whether there is sufficient evidence to conclude that less than 5.5 % of this drug's users experience flulike symptoms as a side effect at the α=0.04 level of significance

It is a one tailed(left tailed hypothesis). We will use z distribution because we are dealing with proportion

using z distribution table for left tailed z critical value at significance level of 0.04

we get

z critical = -1.75

(2) A supervisor thinks this percentage has increased due to increased use of technology in the workplace. So, we have test whether the proportion has increased or not, i.e. it is a right tailed hypothesis for proportion testing with significance level of 0.05

using z distribution table for right tailed z critical value at significance level of 0.05

we get

z critical = 1.64

(3) 95% confidence level means 0.05 significance level because we know that alpha level =1 - confidence level

= 1-0.95= 0.05

We have to test whether the male population proportion is greater in having tattoos at a 95 % confidence level, i.e. it is a right tailed hypothesis for proportion testing with significance level of 0.05

using z distribution table for right tailed z critical value at significance level of 0.05

we get

z critical = 1.64