### 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 $210. At the 0.05 level of significance, can we suggest that the average earnings of this university’s work-study students were significantly higher than the national mean? The null and alternative hypotheses that can be used to suggest that the average earnings of this university’s work-study students were significantly higher than the national mean. Compute the value of the test statistic.
Many cheeses are produced in the shape of a wheel. Because of the differences in consistency between these different types of cheese, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine whether there is a significant difference, at the 10% level, between the weight per wheel of Gouda and Brie cheese. She randomly samples 18 wheels of Gouda and finds the mean is 1.3 lb with a standard deviation of 0.3 lb; she then randomly samples 10 wheels of Brie and finds a mean of 0.95 lb and a standard deviation of 0.21 lb. What is the df and p-value for Heidi's hypothesis of equality? Assume normality. (Give your answer correct to four decimal places.)
A marketing researcher wants to estimate the mean amount spent per year ($) 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…
A new drug is being tested to see if it reduces the frequency of migraines. Study participants were divided into two groups. 49 participants in group 1 received the medication; 42 participants in group 2 received a placebo. After a period of six months, group 1 had a mean of 4 migraines. It is known that the population standard deviation for this group is 1.3 migraines. Group 2 had a mean of 5.4 migraines. The population standard deviation for this group is 1.7 migraines. Can we conclude that the medication reduces the population mean number of migraines? Use αα =0.01. Note: If t-test, then unequal variances are assumed. Question a)Let: μ1μ1 = the population mean number of migraines with the medication μ2μ2 = the population mean number of migraines with the placebo (Step 1) State the null and alternative hypotheses by selecting the appropriate symbol, and identify which tailed test: H0:H0: μ1μ1 μ2μ2 H1:H1: μ1μ1 μ2μ2 Which tailed 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? 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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In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school. For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours. Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours? Perform the appropriate hypothesis test using a significance level of 0.005. What are the hypotheses? What is the test statistic? Is it a z or a t? Find the P-value for this test statistic. How does it compare to the significance level? On the normal curve, indicate the location of the test statistic and the p-value. (label them on the graph) Write…

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