Statistics Confidence Intervals and Significance Test

54 newly hired employees were randomly selected at a major company and asked what the balance was in their savings account. The sample produced a mean of $2,519 with a standard deviation of $942. If we wanted to test the hypothesis that savings account balances for newly hired employees as this company were less than $3,000, what would be the value of the test statistic after conducting the appropriate hypothesis test? Give the appropriate variable of the test statistic and the value rounded to two decimal places.

47 students from Lyndhurst HS and 62 students from Rutherford HS were asked how many times a year they go to American Dream mall. The mean and standard deviation for Lyndhurst was 9.27 and 4.8, while the mean and standard deviation for Rutherford was 12.55 and 6.2. Does this provide convincing evidence at the .01 level that Rutherford HS students go to American Dream mall at least 2 more times a year than Lyndhurst HS students? Show ALL of your work in the box and give the FULL explanation!

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109 randomly selected college students were asked, "Did you select your college because it had a reputation as a 'party school' ?" From those 109, 45 responded yes. At the .05 significance level, what is the correct conclusion after conducting the appropriate hypothesis test to determine if less than half of college students chose their college because it had a reputation as a 'party school'?

• P-value is greater than .05, reject Ho and conclude that less than half of students chose their school because it was a party school.

• P-value is greater than .05, reject Ha and conclude that more than half of students chose their school because it was a party school.

• P-value is less than .05, reject Ho and conclude that less than half of students chose their school because it was a party school.

• P-value is greater than .05, fail to reject Ho and conclude that we do not know if less than half of students chose their school because it was a party school.

35 randomly selected boys and 42 randomly selected girls at Harrison High School were asked: "How many times a day do you charge your cell phone?" After obtaining the appropriate summary statistics from the sample, what would be the appropriate significance test to determine if HHS boys charge their cell phones more frequently than HHS girls?

• 2-proportion Z-Test

• 2-mean T-Test

• Matched pairs T-test

• 1-mean T-Test

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. The data are shown above. Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df = 19?

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• A
• B
• C
• D

A 95% confidence interval was conducted on American adults aged 45-64 and found that the between 15.7% and 19.4% had diabetes as of 2016.

a) What is the population proportion that has diabetes according to this confidence interval? ​ (a)  

b) What was the margin of error associated with this data? ​ (b)  

• 17.55%

• 1.85%

• 11.55

• 5.775

• 11.55%

• 5.775%

Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 95% confidence interval for the parameter.

• 6.593 hours to 7.78 hours

• 6.322 hours to 8.082 hours

• 6.438 hours to 7.947 hours

• 6.174 hours to 8.304 hours

What is the appropriate critical value to use for your margin of error if you are constructing a 99% confidence interval for 2 proportions?