Question

A research center daims that 30% of adults in a ceriain country would travel inlo space on a commercial light if they could afford it. in a random sample of 700 adults in that country. 33% say that they would travel into space on a commercial flight is they could afford in. At a=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below (a) Identify the claim and state H2 and Ha . Identry the claim in this scenario, Select the correct chelce below and fill in the answer box to complete your choice. (Type an integer or a decimal, Do not round ) A. So of adults in the county would travel imto space on a commercial fight it tey could afford it

Answer 1

There is enough evidence to reject the research center's claim at the 0.05 significance level.

Step-by-step explanation:

The null hypothesis (H0) is that 30% of adults in the country would travel into space on a commercial flight if they could afford it, and the alternative hypothesis (Ha) is that this proportion is not 30%. Mathematically, H0: p = 0.30 and Ha: p ≠ 0.30, where p represents the proportion of adults willing to travel into space. The significance level (α) is given as 0.05.

To test the hypothesis, we use a z-test for proportions. In this case, the sample proportion is 33% or 0.33, and the sample size is 700. The formula for the z-test is given by:

`\[ z = \frac{{\hat{p} - p}}{{\sqrt{\frac{{p(1-p)}}{{n}}}}} \]`

Where
`\(\hat{p}\)`is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Substituting the values, we get:

`\[ z = \frac{{0.33 - 0.30}}{{\sqrt{\frac{{0.30(0.70)}}{{700}}}}} \]`

After calculating the z-value, we compare it to the critical z-value at a 0.05 significance level. If the calculated z-value falls outside the critical region, we reject the null hypothesis.

In this case, the calculated z-value exceeds the critical value, indicating that the observed proportion of adults willing to travel into space is significantly different from the claimed 30%. Therefore, there is enough evidence to reject the research center's claim.