Question

A coin is tossed 54 times and 39 heads are observed. Would we infer that this is a fair coin? Use a 97% level confidence interval to base your inference.
The sample statistic for the proportion of heads is:  (3 decimals)

The standard error in this estimate is:  (3 decimals)

The correct z* value for a 97% level confidence interval is:  (3 decimals)

The lower limit of the confidence interval is:  (3 decimals)

The upper limit of the confidence interval is:  (3 decimals)
Based on this confidence interval, it is  --- (A) not plausible (B) plausible --- that the coin is fair.
How would a 99% confidence interval compare to the 97% you constructed? (Select all that apply).

The 99% CI would be wider.

They would have the same center.

They would have different centers.

There is no way to tell how they would compare.

The 99% CI would be narrower.

Answer 1

The statistical software output for this problem is:

Hence,

Standard error = 0.061

z* = 2.170

Lower limit = 0.590

Upper limit = 0.854

Not Plausible

How would a 99% confidence interval compare to the 97% you constructed?

The 99% CI would be wider.

They would have the same center.