Urban traffic congestion throughout the world has been increasing in recent​ years, especially in developing countries. The accompanying table shows the number of minutes that randomly selected drivers spend stuck in traffic in various cities on both weekdays and weekends. Complete parts a through e below.

a) Using alpha = 0.05​, is there significant interaction between the city and time of the​ week?

Identify the hypotheses for the interaction between the city and time of the week. Choose the correct answer below.

A. H0​: City and time of the week do not​ interact, H1​: City and time of the week do interact

B. H0​: μCity ≠ μTime​, H1​: City=μTime

C. H0​: μCity=μTime​, H1​: μCity≠μTime

D. H0​: City and time of the week do​ interact, H1​: City and time of the week do not interact

Find the​ p-value for the interaction between city and time of the week.

​p-value=????

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the interaction between the city and time of the week. Choose the correct answer below.

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that the city and time of the week interact.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

D. Reject the null hypothesis. There is sufficientevidence to conclude that the city and time of the week interact.

​b) Using​ two-way ANOVA and α​=0.05​,does the city have an effect on the amount of time stuck in​ traffic?

Identify the hypotheses to test for the effect of the city. Choose the correct answer below.

A. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all city means are equal

B. H0​: μCity=μTime​, H1​: μCity≠μTime

C. H0​: μCity A≠μCity B≠μCity C≠μCity D​, H1​: μCity A=μCity B=μCity C=μCity D

D. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: μCity A>μCity B>μCity C>μCity D

Find the​ p-value for the effect of the city.

​p-value=???

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the effect of the city. Choose the correct answer below.

A. Reject the null hypothesis. There is sufficient evidence to conclude that not all city means are equal.

B. Do not rejectthe null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Do not rejectthe null hypothesis. There is insufficient evidence to conclude that not all city means are equal.

D. It is inappropriate to analyze because the city and the time of the week interact.

​c) Using​ two-way ANOVA and α​=0.05​, does the time of the week have an effect on the amount of time stuck in​ traffic?

Identify the hypotheses to test for the effect of the time of the week. Choose the correct answer below.

A.H0​: μWeekday=μWeekend​, H1​: Not all time of the week means are equal

B. H0​: μCity=μTime​, H1​:μCity≠μTime

C. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all time of the week means are equal

D. H0​: μWeekday≠μWeekend​, H1​:μWeekday=μWeekend

Find the​ p-value for the effect of the time of the week.

​p-value=???

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the effect of the time of the week. Choose the correct answer below.

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all time of the week means are equal.

B. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is sufficient evidence to conclude that not all time of the week means are equal.

D. It is inappropriate to analyze because the city and the time of the week interact.

​

d) Are the means for weekdays and weekends significantly​ different?

A. Yes​,because there is insufficient evidence to conclude that not all time of the week means are equal.

B. No​, because there is insufficient evidence to conclude that not all time of the week means are equal.

C.Yes​, because there is sufficient evidence to conclude that not all time of the week means are equal.

D. The comparison is unwarranted because the city and the time of the week interact.

4. The university is interested in determining if the proportion of graduates obtaining a first-class degree has changed from 2016 to 2017. Out of 2800 graduates in 2016, 560 obtained a first class degree. In 2017, 805 graduates out of 3500 obtained a first class degree.

1. (a) Write down the method of moments estimates for the proportion of first-class degrees
   in 2016 and 2017, pˆ2016 and pˆ2017.

2. (b) Write down appropriate null and alternative hypotheses for this test.

3. (c) What assumptions are required to conduct your hypothesis test from (b), does this data satisfy them?

4. (d) Calculate a 90% confidence interval for the difference in the proportion of first-class degrees awarded.

5. (e) Using your answer to part (d), or otherwise, test your hypothesis from (b) at the 10% level. You should clearly state the conclusion of your test.

a) An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 177 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.)

2. The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours.

a. What is the probability that a randomly chosen light bulb will last for more than 1800 hours?

b. What percentage of bulbs last between 1350 and 1550 hours?

c. What percentage of bulbs last less than 1.5 standard deviations below the mean lifetime or longer than 1.5 standard deviations above the mean?

d. Find a value k such that 20% of the bulbs last longer than k hours.

A researcher claimed that less than 20% of adults smoke cigarettes. A Gallup survey of 1016
randomly selected adults showed that 17% of the respondents smoke. Is this evidence to support the
researcher’s claim?
(a) What is the sample proportion, ˆp, for this problem?
(b) State the null and alternative hypothesis.
H0 : p =
H1 : p <
Note that you should have written the same number in the null and alternative hypotheses.
This is the value that the researcher is claiming. The sample proportion should never go in the
null or alternative hypotheses. Therefore,the number you have in (a) should not be in the null
or alternative hypothesis.
(c) Calculate the test statistic using the following formula:

z =
pˆ− p
√pq
n
=

where p is the value you stated in the null hypothesis and q is 1 − p.

(d) Now, using either your calculator or the normal distribution table, look up the area that cor-
responds to the z-score you calculated in (c). You don’t need to subtract from 1 because the

alternative hypothesis has < in it. This value is called the p-value.
p-value=
The p-value represents the probability of getting a ˆp of .17 or smaller if the null hypothesis

is true (p=.20). Therefore, if this probability is small then we would doubt that the null hy-
pothesis is true (i.e. if it is not very likely to get ˆp if the true proportion is 20% then this

gives us reason to doubt that p = .2). Thus, small p-values support the alternative hypothesis.
P-values less than .10 or .05 are generally considered small.
(e) Circle the correct answer:
i. The p-value was small which gives us evidence that the actual percent of adults who smoke
is less than 20%.
ii. The p-value was large so we do not have evidence that the actual percent of adults who
smoke is less than 20%.

The answer your circled in (e) is the conclusion to the hypothesis test. We always state conclusions in
context of the problem and we state whether we did or did not have evidence for the alternative hypothesis.
In this case, we did have evidence for the alternative hypothesis that the percentage of adult smokers is
less than 20%.

1. Let  z be a normal random variable with mean 0 and standard deviation 1. What is P(-2.25 <  z < -1.1)?

You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table.

2. The mean of this distribution is _____________.

3. T/F. The probability that the complement of an event will occur is given by P(E') = 1 - P(E)

True

False

4.

A recent survey of local cell phone retailers showed that of all cell phones sold five years ago, 64% had a camera, 28% had a music player, and 22% had both. The probability that a cell phone sold five years ago did not have either a camera or a music player is

5.

The sample standard deviation is related to the sample variance through what functional form?

6.

A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 10 invoices are sampled at random. The binomial probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

7.

Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is 3.4. What is the inverse normal calculation of x?

A coin was flipped 72 times and came up heads 44 times. At the .10 level of significance, is the coin biased toward heads? (a-2) Calculate the Test statistic. (Carry out all intermediate calculations to at least four decimal places. Round your answer to 3 decimal places.) Test statistic

Consider the following hypotheses:

H₀: μ = 38

H_A: μ ≠ 38

Find the p-value for this test based on the following sample information.

a. x¯x¯ = 33; s = 11.9; n = 38

• 0.05 p-value < 0.10
• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

• p-value 0.10

b. x¯x¯ = 43; s = 11.9; n = 38

• 0.01 p-value < 0.02

• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10
• 0.02 p-value < 0.05

c. x¯x¯ = 35; s = 11.1; n = 39

• p-value 0.10

• p-value < 0.01

• 0.01 p-value < 0.02
• 0.05 p-value < 0.10
• 0.02 p-value < 0.05

d. x¯x¯ = 35; s = 11.1; n = 48

• 0.01 p-value < 0.02
• p-value 0.10
• 0.02 p-value < 0.05
• 0.05 p-value < 0.10

• p-value < 0.01

4) An ANOVA model with 4 groups and 10 subjects in each group has a total SS equal to 400, and within SS equal to 300, The MS between and the F value are equal to?

A.  8.57, 11.66

B. 11/66, 30.00

5) For an ANOVA model with 3 groups and total of 27 subjects, the critical value for rejecting the null hypothesis at the 0.05 level of significance is.

A. 99.50

B.  3.40

. Definitions: (do not have to turn in)a. Datab. Statisticsc. Populationd. Samplee. Voluntary response samplef. Parameterg. Statistich. Quantitative datai. Qualitative dataj. Discrete datak. Continuous datal. Nominal level of measurementm. Ordinal level of measurementn. Interval level of measuremento. Ratio level of measurementp. Simple random sampleq. Systematic samplingr. Convenience samplings. Stratified samplingt. Cluster sampling

Let's assume our class represents a normal population with a known mean of 90 and population standard deviation 2. There are 100 students in the class.

a. Construct the 95% confidence interval for the population mean.

b. Interpret what this means.

c. A few students have come in. Now we cannot assume normality and we don't know the population standard deviation. Let the sample mean = 90 and sample standard deviation = 3. Let's make the sample size 20. We can assume alpha to be .05. Construct the 95% confidence interval assuming this new information.

A) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 82 and 100 grams of tea leaves?

B) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the boys whose times are among the top (or fastest) 10% with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? Round to one decimal place.