in 2012 it accepted that 41% or less preferred diesel engine needs a high school statistics student studying a randomly selected group of 51 male found that 23 of them prefer diesel-powered vehicle is that student correct and claiming them that males more prefer diesel powered vehicle?
We might be able to understand your question if you used standard capitalization and punctuation.
To what does the third word, "it," refer?
Doesn't refer to nothing. The rest of the qustion is.. is the student correct in claiming that more males now prefer diesel than 2012.why?
To determine if the student's claim is correct, we can use statistical hypothesis testing. Here's how to do it:
Step 1: State the hypotheses:
The null hypothesis (H₀): The proportion of males who prefer diesel-powered vehicles is equal to or less than 41%.
The alternative hypothesis (H₁): The proportion of males who prefer diesel-powered vehicles is greater than 41%.
Step 2: Calculate the test statistic:
To calculate the test statistic, we use the sample proportion and the null proportion. Let p be the sample proportion (the number of males who prefer diesel-powered vehicles divided by the total sample size):
p = 23/51 = 0.451.
Under the null hypothesis, we assume that the population proportion is 0.41. The test statistic, called z-score, is computed as follows:
z = (p - P₀) / √(P₀ * (1 - P₀) / n),
where P₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.
Substituting the values, we get:
z = (0.451 - 0.41) / √(0.41 * (1 - 0.41) / 51) = 0.041 / 0.067 = 0.612.
Step 3: Determine the p-value:
The p-value is the probability of observing a test statistic as extreme as the one calculated. Since we are conducting a one-tailed test (greater than), we would calculate the area to the right of the observed z-score (0.612) on a standard normal distribution. By consulting a standard normal distribution table or using statistical software, we can find the p-value associated with this test statistic.
Step 4: Compare the p-value with the significance level:
Suppose we choose a significance level (α) of 0.05. If the p-value is less than α, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 5: Make a conclusion:
If the p-value is less than 0.05, we can conclude that there is sufficient evidence to support the claim that more than 41% of males prefer diesel-powered vehicles. However, if the p-value is greater than or equal to 0.05, we do not have enough evidence to support the claim.
So, in order to determine if the student is correct, we need to know the p-value associated with the test statistic (0.612).