the international olympic committee states that the female participate in the 2004 Summer Olympic Games was 42%, even with the new sports for women such as weight lifting, hammer throw, and modern pentathalon being added to the Games. Broadcasting and clothing companies want to change their advertising and marketing strategies if the female participation increases at the next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. Teh sports expert reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may increase? Use a=0.10.

Question

the international olympic committee states that the female participate in the 2004 Summer Olympic Games was 42%, even with the new sports for women such as weight lifting, hammer throw, and modern pentathalon being added to the Games. Broadcasting and clothing companies want to change their advertising and marketing strategies if the female participation increases at the next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. Teh sports expert reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may increase? Use a=0.10.

Answer 1

jkdhd fakjdsh

Answer 2

To determine whether the evidence suggests that the participation rate may increase, we need to conduct a hypothesis test.

First, let's set up our hypothesis:

Null hypothesis (H₀): The participation rate will remain the same or decrease.
Alternative hypothesis (H₁): The participation rate will increase.

Next, let's determine the critical value at a significance level of 0.10.

For this one-sample proportion test, we will be using the z-test. The critical value for a two-tailed test at a significance level of 0.10 is approximately z = ±1.645.

Now, let's calculate the test statistic using the formula:

z = (p - P₀) / √[(P₀ * (1 - P₀)) / n]

where:
p = sample proportion of female athletes
P₀ = hypothesized population proportion under the null hypothesis
n = sample size

Given that the sample size is 454 and there were 202 women in the random sample, the sample proportion can be calculated as:

p = 202 / 454 ≈ 0.445

Since we are testing the hypothesis that the participation rate may increase, we will assume the null hypothesis value of P₀ to be 42% (0.42).

Now, calculating the test statistic:

z = (0.445 - 0.42) / √[(0.42 * (1 - 0.42)) / 454]
≈ 0.025 / √[0.2444 / 454]
≈ 0.025 / √0.0005370964
≈ 0.025 / 0.023166614
≈ 1.08

Since the calculated test statistic (1.08) is less than the critical value (1.645), we fail to reject the null hypothesis.

Therefore, based on the provided evidence, there is not strong enough evidence to suggest that the participation rate may increase.