Final answer:
The pooled sample proportion for the claim regarding cat ownership between men and women, with 110 men sampled (50% owning cats) and 170 women sampled (30% owning), is found to be 0.38 after rounding to two decimal places.
Step-by-step explanation:
To test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats, we need to find the pooled sample proportion (pooled proportion). We have two samples: n1=110 men with 50% owning cats, and n2=170 women with 30% owning cats.
The pooled sample proportion is calculated by taking the total number of successes (men and women who own cats) and dividing it by the total number of trials (the combined sample size of men and women).
In this case, the total number of men who own cats is (0.5 * 110) = 55 and the number of women who own cats is (0.3 * 170) = 51. The combined sample size is 110 + 170 = 280.
The pooled sample proportion is calculated as follows:
Pooled Proportion = (Number of men who own cats + Number of women who own cats) / Total number of trials
Pooled Proportion = (55 + 51) / 280 = 106 / 280 = 0.3786
After rounding to two decimal places, the pooled sample proportion is 0.38.