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.**

A coin is tossed 73 times and 30 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...

Suppose a coin is randomly tossed n = 400 times, resulting in X
= 240 Heads. Answer each of the following; show all work!
(a) Calculate the point estimate, and the corresponding
two-sided 95% confidence interval, for the true probability pi =
P(Heads), based on this sample.
(b) Calculate the two-sided 95% acceptance region for the null
hypothesis H0: pi = 0.5 that the coin is fair.
(c) Calculate the two-sided p-value (without correction term) of
this sample, under the...

(a) Construct a 99% confidence interval for the population
proportion who prefer your client's product.
(b) Would a 95% confidence interval for the same population
proportion be wider or narrower.
(c) The marketing director of your client's company states, "I
am almost certain that our product is preferred by at least 40% of
consumers". Based on your answer to part (a), do you agree with
him? Why or why not?
Consumer ID
Product Preference
1
Competitor
2
Client
3
Competitor...

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