R10.1. Which procedure? For each of the following settings, say which inference procedure from Chapter 8, 9, or 10 you would use. Be specific. For example, you might say, “Two-sample z test for the difference between two proportions.” You do not need to carry out any procedures.
(a) Do people smoke less when cigarettes cost more? A random sample of $500$smokers was selected. The number of cigarettes each person smoked per day was recorded over a one-month period before a $30\%$ cigarette tax was imposed and again for one month after the tax was imposed.
(b) How much greater is the percent of senior citizens who attend a play at least once per year than the percent of people in their twenties who do so?
Random samples of $100$senior citizens and $100$ people in their twenties were surveyed.
(c) You have data on rainwater collected at $16$ locations in the Adirondack Mountains of New York State. One measurement is the acidity of the
water, measured by pH on a scale of $0$to $14$(the pH of distilled water is $7.0$). Estimate the average acidity of rainwater in the Adirondacks.
(d) Consumers Union wants to see which of two brands of calculator is easier to use. They recruit $100$ volunteers and randomly assign them to two
equal-sized groups. The people in one group use Calculator A and those in the other group use Calculator B. Researchers record the time required for each volunteer to carry out the same series of routine calculations (such as figuring discounts and sales tax, totaling a bill) on the assigned calculator.

To find that people smoke less when cigarettes cost more. Since, the number of cigarettes each person smoked per day was recorded over a one-month period before a $30\%$cigarette tax was imposed and again for one month after the tax was imposed.

Since, one proportion: $z$ test/interval with one sample
Two proportions: $z$ test/interval with two sample
One mean: $t$ test/interval with one-sample
Two means: $t$ test/interval or paired $t$ test/interval with two-sample.
To determine whether there is a difference, equality, or an increase or reduction. To estimate the interval in which the true value lies, use an interval. Because the same participants are in both samples, a paired $t$test for a mean difference and an increase is tested.

As a result, for a mean difference, use a paired $t$test.

To determine that how greater is the percent of senior citizens who attend a play at least once per year than the percent of people in their twenties who do so. Let, random samples of $100$senior citizens and $100$people in their twenties were surveyed.

Since, one proportion: $z$ test/interval with one-sample.
Two proportions: $z$ test/interval with two-sample.
One mean: $t$ test/interval with one-sample.
Two means: $t$test/interval or paired $t$ test/interval with two-sample.
To determine whether there is a difference, equality, or an increase or reduction.

To estimate an interval in which the true value lies, use an interval. Because is interested in the estimate of the proportion difference, a two-sample $z$interval is used for a proportion difference.

As a result, for a proportion difference, a two-sample $z$ interval is used.

To estimate the average acidity of rainwater in the Adirondacks. One measurement is the acidity of the water, measured by pH on a scale of $0$to $14$.

Let, One proportion: $z$ test/interval with one-sample.
Two proportions: $z$ test/interval with two-sample.
One mean: $t$ test/interval with one-sample.
Two means: $t$test/interval or paired $t$ test/interval with two-sample.
To determine whether there is a difference, equality, or an increase or reduction.
To estimate the interval in which the true value lies, use an interval.
Because, we are interested in estimating the population mean, will use a one-sample $t$interval for the mean.

As a result, For the mean, one-sample $t$interval.

The people in one group use Calculator A and those in the other group use Calculator B. Researchers record the time required for each volunteer to carry out the same series of routine calculations.

Since, one proportion: $z$ test/interval with one sample.
Two proportions: $z$ test/interval with two-sample.
One mean: $t$ test/interval with one-sample
Two means: $t$test/interval or paired $t$test/interval with two-sample.

To determine whether something is different, equal, or has increased or decreased. To calculate the true value, use an interval.
Because we're trying to estimate the difference between two population means, we'll use a two-sample $t$interval for the mean difference.

As a result, Mean difference $t$ interval with two samples.