Confidence Intervals and Hypothesis Testing

Discuss the importance of standard error in making inferences from the sampling distribution of slopes.

• Standard error does not affect the width of the confidence interval

• Standard error is only relevant for categorical variables, not continuous ones

• Standard error has no impact on the reliability of the slope estimate

• Standard error is important as it quantifies the precision of the slope estimate and influences the confidence interval width, hypothesis testing, and overall reliability of the inference.

How can confidence intervals be used in inference based on the sampling distribution of slopes?

• Confidence intervals provide a range of plausible values for the population slope based on the sample data and its variability.

• Confidence intervals are calculated based on the mean of the sample, not the slope.

• Confidence intervals are used to determine the exact population slope without any margin of error.

• Confidence intervals are only applicable to categorical data, not slopes.

What is the significance of hypothesis testing in the context of sampling distribution of slopes?

• Hypothesis testing in this context is crucial for assessing the reliability and generalizability of the relationship between variables.

• Hypothesis testing is irrelevant in this context

• Hypothesis testing is used to determine the sample size

• Hypothesis testing only applies to categorical variables

• A) Ho: The mean number of days 9th grade students absent is equal to the mean number of days 12th grade students are absent.
  Ha: The mean number of days 9th grade students absent is less than the mean number of days 12th grade students are absent.
• B) Ho: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
• C) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 9th grade students absent is greater than the mean number of days 12th grade students are absent. 
• D) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

• 89.08 < μ < 94.92

• 87.27 < μ < 96.73

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The t distribution is more accurate than a z distribution.

• Clarity ratings for the entire bacth are normally distributed.

• The t-distribution will create a narrower interval than z.

• The standard deviation for the population is unknown.

30 randomly selected students took the Stats final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99% confidence interval for the mean score of all students from which the sample was gathered.

• (89.08, 94.92)

• (87.27, 96.73)

• (87.29, 96.71)

• (87.77, 96.23)

A sample of 30 women finds the mean height to be 62.3 in and the standard deviation to be 1.5 in. Find the margin of error of women's heights with a 95% CL.

• 699

• 0.56

• 0.537

• 19.325

Which of the following does NOT have an affect on the width of a confidence interval?

• Sample mean

• Z*

• standard deviation

• Sample size

The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 13.2,  5.1,  7.5,  8.0,  12.7,  7.6,  13.8,  14.5,  7.7, and 10.5.  Determine a 95 percent confidence interval for the mean time for all players.

• 12.30 < μ < 7.82

•  7.82 < μ < 12.30

• 7.72 < μ < 12.40

• 12.40 < μ < 7.72