Final answer:
To determine if the percentage of people who believe in extraterrestrial life is different from 46%, a hypothesis test is used. The sample proportion from 120 surveyed individuals is compared to the claimed proportion using a z-test for proportions at a significance level of 0.10. The null hypothesis is rejected if the p-value is less than 0.10, indicating a significant difference.
Step-by-step explanation:
The question asks about conducting a hypothesis test to determine if the actual percentage of people who believe in extraterrestrial life is different from a previously stated percentage (46%) based on a sample survey. Given that a scientist surveyed 120 individuals, with 48 affirming belief in life on other planets, we can set up a hypothesis test to compare the sample proportion to the claimed proportion. The null hypothesis (H0) would be that the true proportion (p) equals 0.46 (p = 0.46), while the alternative hypothesis (H1) would be that the true proportion differs from 0.46 (p ≠ 0.46). Using the significance level of alpha = 0.10, we would calculate the test statistic and the p-value to determine if there's enough evidence to reject the null hypothesis.
In this scenario, considering 120 individuals with 48 believers, the sample proportion is 48/120 = 0.40. To carry out the test, we would use the z-test for proportions, as the sample size is large enough. The significance level alpha determines the rejection region. If the p-value obtained is less than alpha, we reject the null hypothesis, indicating that there is sufficient evidence to suggest that the percentage indeed differs from 46%. If the p-value is greater than alpha = 0.10, then we do not reject the null hypothesis, implying that there's insufficient evidence to conclude a difference from 46%.