Question

In: Statistics and Probability

Last year, 46% of business owners gave a holiday gift to their employees. A survey of...

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 45% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.

(a) How many business owners in the survey plan to provide a holiday gift to their employees?
(b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. If required, round your answer to four decimal places. If your answer is zero, enter “0”. Do not round your intermediate calculations.
(c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts has decreased?
We - Select your answer -rejectfail to rejectItem 3  the null hypothesis. We - Select your answer -cancannotItem 4  conclude that the proportion of business owners providing gifts has decreased from 2008 to 2009.
What is the smallest level of significance for which you could draw such a conclusion? If required, round your answer to four decimal places. If your answer is zero, enter “0”. Do not round your intermediate calculations.
The smallest level of significance for which we could draw this conclusion is  ; because p-value - Select your answer -less than or equal togreater thanItem 6  α=0.05, we - Select your answer -rejectfail to rejectItem 7  the null hypothesis.

Solutions

Expert Solution

a)

Sample Size,   n =    60
      
Sample Proportion ,    p̂ = 0.45

business owners in the survey plan to provide a holiday gift to their employees , X=np = 60*0.45 = 27

b)

Ho :   p =    0.46
H1 :   p <   0.46

Standard Error ,    SE = √( p(1-p)/n ) =    0.0643  
          
Z Test Statistic =    Z = ( p̂-p)/SE =    -0.1554  
          
  
p-Value   =   0.4382 [excel function =NORMSDIST(z)]

c)

p value>α ,do not reject null hypothesis           
We fail to reject the null hypothesis. We -cannot conclude that the proportion of business owners providing gifts has decreased from 2008 to 2009.

smallest level of significance for which you could draw such a conclusion=0.4382

The smallest level of significance for which we could draw this conclusion is  ; because p-value -less than or equal to α=0.05, we - -reject the null hypothesis.



Related Solutions

Last year, 46% of business owners gave a holiday gift to their employees. A survey of...
Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees? (b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test...
Last year, 46% of business owners gave a holiday gift to their employees. A survey of...
Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 40% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees? (b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test...
Last year, 46% of business owners gave a holiday gift to their employees. A survey of...
Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees? (b) Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test...
Last year, 45% of business owners gave a holiday gift to their employees. A survey of...
Last year, 45% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 35% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 80 business owners. (A) How many business owners in the survey plan to provide a holiday gift to their employees this year? (B) Suppose the business owners in the sample did as they plan. Compute the p-value...
Last year, 57% of business owners gave a holiday gift to their employees. A survey of...
Last year, 57% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 45% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 80 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees this year? business owners (b) Suppose the business owners in the sample did as they plan. Compute...
In 2013, 30% of business owners gave a holiday gift to their employees. A 2014 survey...
In 2013, 30% of business owners gave a holiday gift to their employees. A 2014 survey of 53 business owners indicated that 19% plan to provide a holiday gift to their employees. Is there reason to believe the proportion of business owners providing gifts has decreased at a=0.05? 1)- What is/are the critical values? 2)- What is the test statistics? 3)- What is the conclusion? Please explain in detail and step by step
Suppose that in the United States last season’s hot holiday gift was the iPad (which is...
Suppose that in the United States last season’s hot holiday gift was the iPad (which is made primarily in China) while this season’s big gift is media content for the iPad (which is made in the U.S.). Determine whether there will be an increase, decrease, or no change for each of the following variables compared to last year.      a. The supply of dollars would decrease  Correctand the demand for dollars would not change  Correct.      b. The exchange rate between the...
In a survey, 10 people were asked how much they spent on their child's last birthday gift.
In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $38 and standard deviation of $8. Construct a confidence interval at a 98% confidence level.  
In a survey, 27 people were asked how much they spent on their child's last birthday gift.
In a survey, 27 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $10. Find the margin of error at a 95% confidence level.Give your answer to two decimal places.
As part of a​ survey, a marketing representative asks a random sample of 3030 business owners...
As part of a​ survey, a marketing representative asks a random sample of 3030 business owners how much they would be willing to pay for a website for their company. She finds that the sample standard deviation is ​$34043404. Assume the sample is taken from a normally distributed population. Construct 9090​% confidence intervals for​ (a) the population variance sigmaσsquared2 and​ (b) the population standard deviation sigmaσ. Interpret the results. ​(a) The confidence interval for the population variance is ​(nothing​,nothing​). ​(Round...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT