Download mean? proportion? relationship? • Mean: one population? two populations?

• What do we want to know about the population?
• What do we want to know about the population?
mean?
• What do we want to know about the population?
mean? proportion?
• What do we want to know about the population?
mean? proportion? relationship?
• What do we want to know about the population?
mean? proportion? relationship?
• Mean:
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population?
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population:
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
No
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
No → t-procedure
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
No → t-procedure (t-critical value table)
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
No → t-procedure (t-critical value table)
∗ Two population:
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
No → t-procedure (t-critical value table)
∗ Two population: t-procedure
• What do we want to know about the population?
mean? proportion? relationship?
• Mean: one population? two populations?
∗ One population: do we know the population standard
deviation σ?
Yes → z-procedure (standard normal table)
No → t-procedure (t-critical value table)
∗ Two population: t-procedure
• Proportion:
• Proportion: one population?
• Proportion: one population? two populations?
• Proportion: one population? two populations?
∗ One population:
• Proportion: one population? two populations?
∗ One population: z-procedure
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population:
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population: z-procedure
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population: z-procedure
confidence interval:
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population: z-procedure
confidence interval: when can we use large-sample C.I. /
plus four C.I.?
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population: z-procedure
confidence interval: when can we use large-sample C.I. /
plus four C.I.?
test of significance:
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population: z-procedure
confidence interval: when can we use large-sample C.I. /
plus four C.I.?
test of significance: conditions;
• Proportion: one population? two populations?
∗ One population: z-procedure
if we want to estimate p by confidence interval, then how
large is our sample?
both number of successes and number of failures are at
least 15 → large-sample C.I.
number of uccesses or number of failures is less than 15
but sample size is at least 10 → plus four C.I.
conditions for test of significance
∗ Two population: z-procedure
confidence interval: when can we use large-sample C.I. /
plus four C.I.?
test of significance: conditions; pooled sample proportion
• Relationship:
• Relationship: χ2 test
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table:
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit:
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval:
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator?
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error?
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error? standard error?
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error? standard error?
• Test of significance:
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error? standard error?
• Test of significance:
hypotheses (null & alternative)
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error? standard error?
• Test of significance:
hypotheses (null & alternative) → test statistic
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error? standard error?
• Test of significance:
hypotheses (null & alternative) → test statistic → P-value
• Relationship: χ2 test
How to calculate the test statistic χ2 ?
χ2 =
X (observed count − expected count)2
expected count
∗ Two-way table: how to calculate the expected count?
∗ Goodness-of-fit: how to calculate the expected count?
• Confidence interval: estimator ± margin of error
estimator? margin of error? standard error?
• Test of significance:
hypotheses (null & alternative) → test statistic → P-value →
conclusion