Question

In: Math

Researchers for an advertising company are interested in determining if people are more likely to spend...

Researchers for an advertising company are interested in determining if people are more likely to spend more money on beer if advertisers put more beer ads on billboards in a neighborhood in Philadelphia. They estimate that 250 people will view their billboard in one week. They determine that the total number of residents in the neighborhood is 600. So, the residents who have not viewed the billboard are in the control group. The researchers determine that those who did view the ads spent $24 per week on beer and those who did not view the ads spent $16 per week on beer.

Calculate the treatment effect.

Calculate the standard error (hint: the researchers determined the Std. Dev. for the control is $1.3 and the Std. Dev. for the treatment is $0.90)

Calculate the t-statistic.

Can we reject OR fail to reject the null hypothesis? Explain why.

Expert Solution

Given -

For Control -

N = 350

mean = $16

standard deviation = $1.3

For Test -

N = 250

mean = $24

standard deviation = $0.9

A -

treatment effect -

increase in sales/original sales

= 24 - 16/16

= 50%

=> There is 50% lift in sales or the treatment effect is 50%

B -

Since the population standard deviation is seldom known, the standard error of the mean is usually estimated as the sample standard deviation divided by the square root of the sample size.

standard error of control = 1.3/sqrt(350)

= $0.069

standard error of test = 0.9/sqrt(250)

= $0.056

standard error of difference = sqrt(1.3²/350 + 0.9²/250)

= 0.0898

C -

t -test = (sample mean 1 – sample mean 2)/[ sqrt ( s1^2/n1 + s2^2/n2) ]

= 24 - 16/0.0898

= 8/0.0898

= 89.08

D -

This is a one tailed hypothesis since we know we have to calculate whether increase in sales is significant or not

Null hypothesis - There is no significant increase in sales from treatment group as compared to the control group

Alternate hypothesis - There is significant increase in sales from treatment group as compared to the control group

The t critical value at 0.001 significance level and degrees of freedom = 598 is 2.6

The result is significant even at 0.001 significance level

Hence, we can reject the null hypothesis and go with our alternate hypothesis

milcah answered 8 months ago

Do consumers spend more on a trip to Target compared to Walmart? Suppose researchers interested in...

Do consumers spend more on a trip to Target compared to Walmart? Suppose researchers interested in this question collected a random sample from 80 Target customers and 85 Walmart customers by asking customers for their purchase amount as they left the stores. The 80 Target customers have the mean purchase amount $53 and the standard deviation $19. The 85 Walmart customers have the mean purchase amount $45 and the standard deviation $21. [2 points] Is the data collected from independent...

Do consumers spend more on a trip to Store A or Store B? Suppose researchers interested...

Do consumers spend more on a trip to Store A or Store B? Suppose researchers interested in this question collected a systematic sample from 85 Store A customers and 82 Store B customers by asking customers for their purchase amount as they left the stores. The data collected is summarized by the accompanying table. Suppose researchers decide to test the hypothesis that the means are equal. The degrees of freedom formula gives 164.33 Test the null hypothesis at 0.05 Store...

1. Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in...

1. Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in this question collected a systematic sample from 85 Walmart customers and 80 Target customers by asking customers for their purchase amount as they left the stores. The data collected are summarized in the table below. Walmart Target sample size 85 80 sample mean $45 $53 sample std dev $20 $18 a. Check the conditions to create a confidence interval for the difference in...

1. When interest rates are low, people are more likely to spend (or borrow) and less...

1. When interest rates are low, people are more likely to spend (or borrow) and less likely to save. This is consistent with the slopes of both the demand and supply in the loanable funds market. True False 2. The loanable funds market is a fundamental piece of a country's ability to grow and develop. True False 3. Which of the following would SHIFT the demand for loanable funds to the RIGHT (i.e. INCREASE). Select all that apply. Expectations that...

A sales manager is interested in determining the relationship between the amount spent on advertising and...

A sales manager is interested in determining the relationship between the amount spent on advertising and total sales. the manger collects data for the past months and runs a regression of sales on advertising expenditures. The results wıth some missing values are presented below. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.492 0.242 0.208 40.975 ANOVA df SS MS F Significance Regression Residual Total 1 Coefficients Standard Error t Stat P-value Constant Advertising To test the...

Researchers interested in determining if there is a relationship between anxiety and religiosity conducted the following...

Researchers interested in determining if there is a relationship between anxiety and religiosity conducted the following study. Subjects completed a 5 point anxiety item (high score = high anxiety) and also completed a 15 item checklist designed to measure an individual’s degree of religiosity (belief in a particular religion, regular attendance at religious services, etc). A high score indicates greater religiosity. Sample data from 10 subjects are provided below. Can you predict anxiety (y) from religiosity (x)? First determine the...

Researchers are interested in determining if men and women’s hearts tend to be different sizes. In...

Researchers are interested in determining if men and women’s hearts tend to be different sizes. In a sample of 30 males, the mean diameter of the heart was 13.21 cm with a standard deviation of 1.05. Among 32 females, the mean diameter of the heart was found to be 11 cm with a standard deviation of 1.01. Construct a two-sided 95% confidence interval for the difference between the two means, assuming equal variance. Give an interpretation of the confidence interval.

Lacey is interested in determining whether people who have experienced a traumatic event experience more sleep...

Lacey is interested in determining whether people who have experienced a traumatic event experience more sleep disturbances than people who have not experienced such an event. She distributes a sleep disturbance survey to 103 individuals wh o experienced a traumatic event and to 98 people who had never experienced a traumatic event. If the mean score on the survey was 13.20 ( s = 3.51) for the trauma group and 8.10 ( s = 2.17 ) for the non-trauma group,...

Researchers were interested in determining whether there was a difference in crime rates in areas where...

Researchers were interested in determining whether there was a difference in crime rates in areas where there is high youth unemployment vs low youth unemployment. Alpha (level of significance) was set at .05. State the null and alternate hypotheses. What is the independent variable? What is the dependent variable? Complete the table below: Low Youth Unemployment High Youth Unemployment Sample Size Sample Mean Sample Standard Deviation Estimated Standard Error Group Statistics High Youth Unemployment N Mean Std. Deviation Crime rate...

The University is interested in determining if the number of people coming to work by pedal...

The University is interested in determining if the number of people coming to work by pedal bicycle has changed from 2016 to 2017. Over the course of a week (Mon-Sun) they count the number of cyclists who enter campus at the North campus cycle path entrance between 8am-10am each day. The University have data from the same week in 2016. The counts for each day of the week for 2016 and 2017 are given in Table: Mon Tues Wed Thurs...