Question

Can someone help me with these problems? Thank you.

1. True or False. (a) Confidence intervals are a useful alternative to gathering data from an entire population. (b) As the level of confidence increases, the width of the confidence interval should decrease. (c) As the sample size increases, the width of the confidence interval should decrease. (d) Rejecting the null hypothesis means that you should reject the claim. (e) Injecting bleach is an effective way to treat Covid-19. 2. You wish to estimate, with 95% confidence, the mean time it takes to pet all of the cats at the animal shelter. You observe 13 random people and find that the average amount of time it took to pet the cats was 23 minutes with a standard deviation of 24 minutes. Assume the population is normally distributed. Compute the confidence interval. 3. You wish to estimate, with 99% confidence, the proportion of Hancock students who love statistics more than life itself. President Walthers demands that the estimate must be accurate to within 3% of the population proportion. (a) Assume no preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size using a prior survey that found that 13% of Hancock students love statistics more than life itself.

Answer 1

Question 1:

(a) True

Confidence intervals are an alternative to hypothesis testing.

(b) False

As the level increases, the width increases.

(c) True

(d) False

The claim can be the null or alternative hypothesis.

(e) False

Question 2:

The 95% confidence interval will be:

= x ± t*(s/√n)

= 23 ± 2.18*(2.4/√13)

= (21.55, 24.45)

Question 3:

(a) n = (2.576/0.03)^2*0.5*(1 - 0.5) = 1844

(b) n = (2.576/0.03)^2*0.13*(1 - 0.13) = 834

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