### Statistical Analysis of Sales CallsThe Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that sales representatives make an average of 40 sales calls per week on professors. Some representatives believe this estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42, with a standard deviation of 2.1 calls. Using a significance level of 0.05, can we conclude that the mean number of calls per salesperson per week is more than 40?#### Hypotheses- $ H_0: \mu \leq 40 $- $ H_1: \mu > 40 $#### Steps to the Analysis1. **Compute the Value of the Test Statistic**: - **Instructions**: Round your answer to three decimal places. - **Result Box**: - Value of the test statistic: [ _ ]2. **Decision Regarding $ H_0 $**: - **Prompt**: State your decision. - **Result Box**: - H0: The mean number of calls is [ _ ] than 40 per week.#### Explanation of Concepts- **Test Statistic**: A measure used in statistical hypothesis testing. It is calculated from the sample data and used to decide whether to reject the null hypothesis ($ H_0 $) in favor of the alternative hypothesis ($ H_1 $).- **Significance Level (0.05)**: The probability of rejecting the null hypothesis when it is actually true. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.- **Decision Rule**: If the test statistic falls into the rejection region (greater than the critical value), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.This procedure outlines a hypothesis test aimed at determining whether the mean number of sales calls exceeds the historical average of 40 calls per week. It utilizes a sample mean and known standard deviation to evaluate the claim statistically.

From the information, given thatThe claim is to test whether the mean number of calls per…

Answered: The Rocky Mountain district sales…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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During 2008, college work-study students earned a mean of $1478. Assume that a sample consisting of 25 of the work-study students at a large university was found to have earned a mean of $1503 during that year, with a standard deviation of $210. At the 0.05 level of significance, can we suggest that the average earnings of this university’s work-study students were significantly higher than the national mean? The null and alternative hypotheses that can be used to suggest that the average earnings of this university’s work-study students were significantly higher than the national mean. Compute the value of the test statistic.
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During 2008, college work-study students earned a mean of $1478. Assume that a sample consisting of 25 of the work-study students at a large university was found to have earned a mean of $1503 during that year, with a standard deviation of $210. Formulate the null and alternative hypotheses that can be used to suggest that the average earnings of this university’s work-study students were significantly higher than the national mean
A marketing researcher wants to estimate the mean amount spent per year ($) on a web site by membership member shoppers. Suppose a random sample of 100 membership member shoppers who recently made a purchase on the web site yielded a mean amount spent of $55 and a standard deviation of $52. Complete parts (a) and (b) below. a. Is there evidence that the population mean amount spent per year on the web site by membership member shoppers is different from $51? (Use a 0.01 level of significance.) State the null and alternative hypotheses. Ho: H (Type integers or decimals. Do not round. Do not include the $ symbol in your answer.) Identify the critical value(s). The critical value(s) is/are (Type an integer or a decimal. Round to two decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic. The test statistic, 1STAT, is (Type an integer or a decimal. Round to two decimal places as needed.) State the conclusion. Ho. There is evidence that the…
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You were told that the mean daily cost of a hotel room in downtown St. Louis is $120. You will be needing to rent a hotel room there in the near future and you want to find the best rate. You randomly select a sample of 18 hotel rooms and find that the average cost is $121.33 with a standard deviation of $18.046. At the α = 0.05 significance level, determine if there is enough evidence to reject the claim. What is the decision for this hypothesis test? You were told that the mean daily cost of a hotel room in downtown St. Louis is $120. You will be needing to rent a hotel room there in the near future and you want to find the best rate. You randomly select a sample of 18 hotel rooms and find that the average cost is $121.33 with a standard deviation of $18.046. At the α = 0.05 significance level, determine if there is enough evidence to reject the claim. What is the decision for this hypothesis test? Reject the null because the test statistic is in the critical region and the…
A marketing researcher wants to estimate the mean amount spent per year ($) on a web site by membership member shoppers. Suppose a random sample of 100 membership member shoppers who recently made a purchase on the web site yielded a mean amount spent of $58and a standard deviation of $55.Complete parts (a) and (b) below. a. Is there evidence that the population mean amount spent per year on the web site by membership member shoppers is different from $51? (Use a 0.01 level of significance.) State the null and alternative hypotheses.
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Beer Drinking. The mean annual consumption of beer per person in the US is 22.0 gallons . A random sample of 300 Washington D.C. residents yielded a mean annual beer consumption of 27.8 gallons. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean annual consumption of beer per person for the nation’s capital differs from the national mean? Assume that the standard deviation of annual beer consumption for Washington D.C. residents is 55 gallons.
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