Mathematics Homework Help

I’m working on a statistics multi-part question and need an explanation and answer to help me learn.

1). Confidence Intervals: Determine 95% confidence interval for the true proportion of
successes in each of the following scenarios:
a. We conduct 100 trials and observe 62 successes.
b. We conduct 200 trials and observe 124 successes.
c. We conduct 600 trials and observe 372 successes.
What do you notice about the confidence intervals as the sample size increases? How is this
connected to the Law of Large Numbers?
2). Comparing Service Times
a. The drive-through service times were recorded for 52 randomly selected customers at a
Burger King restaurant. Those times had a mean of 181.3 sec and a standard deviation
of 82.2 sec. Construct a 95% confidence interval estimate of the population mean.
b. The drive-through service times were recorded for 95 randomly selected customers at a
McDonald’s restaurant Those times had a mean of 127.8 sec and a standard deviation
of 60.6 sec. Construct a 95% confidence interval estimate of the population mean.
c. Compare and interpret the results. Does it appear that either restaurant has better
performance. Why or why not?
3). Sales: your company wants to improve sales. Past sales data indicate that the
average sale was $100 per transaction. After training your sales force, recent sales data
(taken from a sample of 25 salesmen) indicates an average sale of $130, with a
standard deviation of $15. Did the training work? Test your hypothesis at a 5%
significance level.
4). Sleep: We want to test whether the mean amount that college students sleep exceeds the
recommended minimum of 7 hours per night. A researcher surveys 1550 college students and
finds the mean to be 6.83 hours with a standard deviation of .23 hours.
a. What specifically was the data collected in the study?
b. Is this data qualitative or quantitative?
c. What command would you do in StatCrunch? Z-stat, T-stat, Proportion stat
d. State the exact sentence in the problem that indicates the direction of the symbol
that will be used in Ha. Will the symbol be <, > or ≠?
e. State the null and alternative hypotheses (Ho and Ha) in symbol form.