Practice Quiz 4
1) A company randomly surveys 15 VIP customers and records their customer
satisfaction scores out of a possible 100 points. Based on the data provided,
calculate a 90% confidence interval to estimate the true satisfaction score of all
VIP customers.
First calculate the mean and standard deviation of the sample, which you can do in
Excel using either the descriptive statistics tool or the AVERAGE and STDEV.S
functions. The mean and standard deviation are approximately 76.60 and 11.28
respectively. Since the sample size is only 15, use the function CONFIDENCE.T(alpha,
standard_dev, size) to find the margin of error using the t-distribution. Here, this is
approximately CONFIDENCE.T(0.1,11.28,15)=5.13. The lower bound of the 90%
confidence interval is the mean minus the margin of error, 76.60–5.13=71.47. The upper
bound of the 90% confidence interval is the mean plus the margin of error,
76.60+5.13=81.73. You must link directly to values in order to obtain the correct answer.
2) The owner of an ice cream shop wants to determine whether there is a
relationship between ice cream sales and temperature. The owner collects data
, on temperature and sales for a random sample of 30 days and runs a regression
to determine if there is a relationship between temperature (in degrees) and ice
cream sales. The p-value for the two-sided hypothesis test is 0.04. How would
you interpret the p-value?
If there is no relationship between temperature and sales, the chance of selecting a
sample this extreme would be 4%.
CORRECT
Correct. The null hypothesis is that there is no relationship. The p-value indicates how
likely we would be to select a sample this extreme if the null hypothesis is true.
If there is a relationship between temperature and sales, the chance of seeing a
regression coefficient this large would be 4%.
Incorrect. The alternative hypothesis is that there is a relationship. The p-value indicates
how likely we would be to select a sample this extreme if the null hypothesis is true.
There is a 4% chance that there is a relationship between temperature and revenue.
Incorrect. The p-value refers to how likely we would be to select a sample this extreme if
the null hypothesis is true, not the likelihood of the null hypothesis being true. A
hypothesis test tests whether or not there is a relationship between variables. Alone, the
p-value provides information about the occurrence of a specific sample, but does not
specify the probability of a relationship occurring (or not) between two variables in the
population.
There is a 4% chance that there is no relationship between temperature and revenue.
Incorrect. The p-value refers to how likely we would be to select a sample this extreme if
the null hypothesis was true, not the likelihood of the null hypothesis being true. A
hypothesis test tests whether or not there is a relationship between variables. Alone, the
p-value provides information about the occurrence of a specific sample, but does not
specify the likelihood probability of a relationship occurring (or not) between two
variables in the population.
3)
, Below is a partial regression output table, which of the following values most likely
belongs in the Lower 95% cell for the independent variable in the output table?
-6.01
Since the p-value, 0.3956, is greater than 0.05, the linear relationship is not significant at
the 95% confidence level. Therefore, the 95% confidence interval of the slope must
contain zero. The confidence interval is centered around the slope of 1.78, so the lower
and upper bounds must be equally distant from the slope. The slope, 1.78, is not in the
middle of -6.01 and 6.01.
-2.45
CORRECT
Since the p-value, 0.3956, is greater than 0.05, the linear relationship is not significant at
the 95% confidence level. Therefore, the 95% confidence interval of the slope must
contain zero. The confidence interval is centered around the slope of 1.78, so the lower
and upper bounds must be equally distant from the slope. The Upper 95% minus the
slope is 6.01–1.78=4.23, so the Lower 95% is 1.78–4.23=-2.45.
1.78
1.78 is the predicted value of the coefficient. The confidence interval must be centered
on 1.78.
2.45
Since the p-value, 0.3956, is greater than 0.05, the linear relationship is not significant at
the 95% confidence level. Therefore, the 95% confidence interval of the slope must
contain zero. The interval between 2.45 and 6.01 does not contain zero.
The answer cannot be determined without further information
The Lower 95% can be found by calculating the difference between the Upper 95% and
the slope, then subtracting that difference from the slope.
1) A company randomly surveys 15 VIP customers and records their customer
satisfaction scores out of a possible 100 points. Based on the data provided,
calculate a 90% confidence interval to estimate the true satisfaction score of all
VIP customers.
First calculate the mean and standard deviation of the sample, which you can do in
Excel using either the descriptive statistics tool or the AVERAGE and STDEV.S
functions. The mean and standard deviation are approximately 76.60 and 11.28
respectively. Since the sample size is only 15, use the function CONFIDENCE.T(alpha,
standard_dev, size) to find the margin of error using the t-distribution. Here, this is
approximately CONFIDENCE.T(0.1,11.28,15)=5.13. The lower bound of the 90%
confidence interval is the mean minus the margin of error, 76.60–5.13=71.47. The upper
bound of the 90% confidence interval is the mean plus the margin of error,
76.60+5.13=81.73. You must link directly to values in order to obtain the correct answer.
2) The owner of an ice cream shop wants to determine whether there is a
relationship between ice cream sales and temperature. The owner collects data
, on temperature and sales for a random sample of 30 days and runs a regression
to determine if there is a relationship between temperature (in degrees) and ice
cream sales. The p-value for the two-sided hypothesis test is 0.04. How would
you interpret the p-value?
If there is no relationship between temperature and sales, the chance of selecting a
sample this extreme would be 4%.
CORRECT
Correct. The null hypothesis is that there is no relationship. The p-value indicates how
likely we would be to select a sample this extreme if the null hypothesis is true.
If there is a relationship between temperature and sales, the chance of seeing a
regression coefficient this large would be 4%.
Incorrect. The alternative hypothesis is that there is a relationship. The p-value indicates
how likely we would be to select a sample this extreme if the null hypothesis is true.
There is a 4% chance that there is a relationship between temperature and revenue.
Incorrect. The p-value refers to how likely we would be to select a sample this extreme if
the null hypothesis is true, not the likelihood of the null hypothesis being true. A
hypothesis test tests whether or not there is a relationship between variables. Alone, the
p-value provides information about the occurrence of a specific sample, but does not
specify the probability of a relationship occurring (or not) between two variables in the
population.
There is a 4% chance that there is no relationship between temperature and revenue.
Incorrect. The p-value refers to how likely we would be to select a sample this extreme if
the null hypothesis was true, not the likelihood of the null hypothesis being true. A
hypothesis test tests whether or not there is a relationship between variables. Alone, the
p-value provides information about the occurrence of a specific sample, but does not
specify the likelihood probability of a relationship occurring (or not) between two
variables in the population.
3)
, Below is a partial regression output table, which of the following values most likely
belongs in the Lower 95% cell for the independent variable in the output table?
-6.01
Since the p-value, 0.3956, is greater than 0.05, the linear relationship is not significant at
the 95% confidence level. Therefore, the 95% confidence interval of the slope must
contain zero. The confidence interval is centered around the slope of 1.78, so the lower
and upper bounds must be equally distant from the slope. The slope, 1.78, is not in the
middle of -6.01 and 6.01.
-2.45
CORRECT
Since the p-value, 0.3956, is greater than 0.05, the linear relationship is not significant at
the 95% confidence level. Therefore, the 95% confidence interval of the slope must
contain zero. The confidence interval is centered around the slope of 1.78, so the lower
and upper bounds must be equally distant from the slope. The Upper 95% minus the
slope is 6.01–1.78=4.23, so the Lower 95% is 1.78–4.23=-2.45.
1.78
1.78 is the predicted value of the coefficient. The confidence interval must be centered
on 1.78.
2.45
Since the p-value, 0.3956, is greater than 0.05, the linear relationship is not significant at
the 95% confidence level. Therefore, the 95% confidence interval of the slope must
contain zero. The interval between 2.45 and 6.01 does not contain zero.
The answer cannot be determined without further information
The Lower 95% can be found by calculating the difference between the Upper 95% and
the slope, then subtracting that difference from the slope.
