Final answer:
The student is inquiring about conducting a hypothesis test to determine if the proportion of people who dream in color now is different than in the 1940's. They are to establish a null hypothesis of no change and an alternative hypothesis of a difference, and ascertain the critical value for a chosen significance level, which is ±1.96 for a two-tailed test at the 0.05 level.
Step-by-step explanation:
The student is asking whether there is evidence to show that the proportion of people who dream in color is different than the proportion in the 1940's based on a recent study of a random sample of 113 people. To establish this, a hypothesis test can be conducted. The null hypothesis (H0) would state that the current proportion is equal to the 1940's proportion (29%), and the alternative hypothesis (H1) would state that the current proportion is different from that of the 1940's.
To determine the critical value for this hypothesis test, we need to decide on a significance level (usually 0.05 for a 95% confidence interval) and whether it's a one-tailed or two-tailed test. Since we are checking for a difference without directional specification, this would be a two-tailed test. The critical value(s) can then be obtained from a z-table corresponding to the chosen significance level.
In this case, for a 0.05 significance level in a two-tailed test, each tail would contain 2.5% of the probability, thus the critical values would be approximately ±1.96.