Question

Using R script code for these questions. 1. A fire department aims to respond to fire calls in 4 minutes or less, on average. Response times are normally distributed with a standard deviation of 1 minute. Would a sample of 18 fire calls with a mean response time of 4.5 minutes provide sufficient evidence to show that the goal is not being met at the significance level α = .01? Is this a left-tailed, right-tailed, or two-tailed test? Formulate null and alternative hypothesis. Compute the appropriate test statistic and critical value using R. What is the statistical decision? Interpret the results. 2. The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased. flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199, 193, 209, 215, 192, 179, 196, 225, 199, 196, 210, 199, 188, 174, 176, 202, 195, 195, 208, 222, 221) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd(). Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis. What is the statistical decision at the significance level α = .01? Run the appropriate test if the population standard deviation was not known. What is the test statistic? What is the critical value? What is the statistical decision at significance level α = .01? 3. The target activation force of the buttons on a clicker is 1.967 newtons. Variation exists in activation force due to the nature of the manufacturing process. A sample of 9 clickers showed a mean activation force of 1.88 newtons. The population standard deviation is known to be 0.145 newton. Too much force makes the keys hard to click, while too little force means the keys might be clicked accidentally. We want to use an appropriate hypothesis test to detect excessive deviations in either direction. What is the appropriate hypothesis test? What is the test statistic value? At α = .05, does the sample indicate a significant deviation from the target?

          Using R script code for these questions. 
1. A fire department aims to respond to fire calls in 4 minutes
or less, on average. Response times are normally distributed with a
standard deviation of 1 minute. Would a sample of 18 fire calls
with a mean response time of 4.5 minutes provide sufficient
evidence to show that the goal is not being met at the significance
level α = .01? Is this a left-tailed,
right-tailed, or two-tailed test? Formulate null and alternative
hypothesis. Compute the appropriate test statistic and critical
value using R. What is the statistical decision? Interpret the
results.
2. The mean arrival rate of flights at Philadelphia
International Airport is 195 flights or less per hour with a
historical standard deviation of 13 flights. To increase arrivals,
a new air traffic control procedure is implemented. In the next 30
days, the arrival rate per day is given in the data vector below
called flights. Air traffic control manager wants to test if there
is sufficient evidence that arrival rate has increased.
flights <-
c(210, 215,     200,     189,     200,     213,     202,     181,     197,     199,
193,     209,     215,     192,     179,     196,     225,     199,     196,     210,
199,     188,     174,     176,     202,     195,     195,     208,     222,     221)
Find sample mean and sample standard deviation of arrival rate
using R functions mean() and sd().
Is this a left-tailed, right-tailed or two-tailed test?
Formulate the null and alternative hypothesis. 
 What is the statistical decision at the significance
level α = .01? 
 Run the appropriate test if the population standard
deviation was not known. What is the test statistic? What is the
critical value? What is the statistical decision at significance
level α = .01?
3. The target activation force of the buttons on a clicker is
1.967 newtons. Variation exists in activation force due to the
nature of the manufacturing process. A sample of 9 clickers showed
a mean activation force of 1.88 newtons. The population standard
deviation is known to be 0.145 newton. Too much force makes the
keys hard to click, while too little force means the keys might be
clicked accidentally. We want to use an appropriate hypothesis test
to detect excessive deviations in either direction. What is the
appropriate hypothesis test? What is the test statistic value? At α
= .05, does the sample indicate a significant deviation from the
target?

Added by Jesse M.

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