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A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 751 doors is made, and it is found that they have a mean of 2047 millimeters with a standard deviation of 32. Is there evidence at the 0.1 level that the doors are too short and unusable?
State the null and alternative hypotheses for the above scenario.

A group of local businessmen is thinking about developing land into a shopping mall. To evaluate the desirability of the location, they count the number of shoppers who visit the neighboring shopping center each day. A random sample of 55 days reveals a daily average of 91 shoppers with a standard deviation of 46 shoppers. The businessmen will develop the land if the average number of shoppers per day is more than 80. Based on the sample data, should the businessmen develop the land? Perform a hypothesis test and use a significance level of α=0.01
. Assume the population of the number of daily shoppers is approximately normally distributed.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=80: μ ? 80
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

The mayor of a town believes that over 49% of the residents favor annexation of an adjoining bridge. Is there sufficient evidence at the 0.01 level to support the mayor's claim? After information is gathered from 320 voters and a hypothesis test is completed, the mayor decides to reject the null hypothesis at the 0.01

What is the conclusion regarding the mayor's claim?

A hospital director is told that 21% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is above the expected percentage. A sample of 240 patients found that 60 were uninsured. At the 0.01 level, is there enough evidence to support the director's claim?

State the null and alternative hypotheses.
b. Find the value of the test statistic. Round your answer to two decimal places.
c. Specify if the test is one-tailed or two-tailed.
d. Determine the P-value of the test statistic. Round your answer to four decimal places.
e. Identify the value of the level of significance.
f. Make the decision to reject or fail to reject the null hypothesis
g. State the conclusion of the hypothesis test.

Doing Mixed Effects Models
Qn1. Recall our file websearch3.csv. If you have not done so already, please download if from the course materials. This file describes a study of the number of searches people did with various search engines to successfully find 100 facts on the web. You originally analyzed this data with a one-way repeated measures ANOVA. Now you will use a linear mixed model (LMM). Let’s refresh our memory: How many subjects took part in this study?

Qn2. To the nearest hundredth (two digits), how many searches on average did subjects require with the Google search engine?

Qn3. Conduct a linear mixed model (LMM) on Searches by Engine. To the nearest ten-thousandth (four digits), what is the p-value of such a test? Hint: use the lme4 library and its lmer function with the subject as random effect. The use the car library and its Anova function with type = 3 and test.statistic = “f”. Prior to either, set sum-to-zero contrasts for engine.
Qn4. In light of your p-value result, are post hoc pairwise comparisons among levels of Engine justified, strictly speaking?


Qn5. Regardless of your answer to the previous question, conduct simultaneous pairwise comparisons among all levels of Engine. Correct your p-values with Holm’s sequential Bonferroni procedure. To the nearest ten-thousandth (four digits), what is the lowest corredted p-value resulting from such tests? Hint: use the multcomp library and its mcp function from within a call to its glht function.

This questions uses the r statistics programming software, if you are looking for someone to help with this question, then do not hesitate to contact MyMathLab answers .