Question

In: Statistics and Probability

Visit Jeju ~ In South Korea, “Jeju” is a famous holiday destination with breathtaking scenic views....

Visit Jeju ~ In South Korea, “Jeju” is a famous holiday destination with breathtaking scenic views. A travel agent in Jeju wants to know the satisfaction levels of tourists who visit the island. The travel agent surveyed 45 tourists at random and constructed a 95% confidence interval for the proportion of tourists who were extremely satisfied with their Jeju visit to be (0.5289, 0.8044).

Which of the following statements are true? Select all the that apply.

Question 17 options:

A 99% confidence interval calculated using the same data will include more plausible values for the actual population proportion.

If the sample size had been double the sample size in the scenario above, then the 95% confidence interval would be half as wide as the one stated above.

If a different sample of the same size were to be selected, then there is a 95% chance that the new sample proportion will lie inside the confidence interval stated above.

If we took several samples of the same size as the scenario given above and constructed 95% confidence intervals for population proportion, then it is reasonable to expect 95% of these confidence intervals to contain the actual population proportion.

A 90% confidence interval for the population proportion calculated using the same data will be wider than the interval stated above.

If a different sample of the same size were to be selected and a 95% confidence interval constructed, then there is a 95% chance that the actual population proportion will lie inside the new confidence interval.

Solutions

Expert Solution

Since the 99% confidence interval will be wider than 95% confidence interval,  A 99% confidence interval calculated using the same data will include more plausible values for the actual population proportion.

If the sample size had been double the sample size, the standard error (and margin of error) will reduce by factor of . So, the second statement is False.

95% confidence interval is not related with the probability that the new sample proportion will lie inside the confidence interval stated above. The third statement is False.

The fourth statement is the correct interpretation of 95% confidence interval.

A 90% confidence interval for the population proportion calculated using the same data will be narrower than the interval stated above, because the critical value of z will be less for 90% confidence interval.

It is correct to say that there is a 95% chance that the confidence interval you calculated contains the actual population proportion.

The true statements are -

A 99% confidence interval calculated using the same data will include more plausible values for the actual population proportion.

If we took several samples of the same size as the scenario given above and constructed 95% confidence intervals for population proportion, then it is reasonable to expect 95% of these confidence intervals to contain the actual population proportion.

orchestra answered 1 year ago
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