isds 2000 part 3

A researcher wants the true mean weekly grocery spending of all households in a city. Which quantity is the parameter?

The mean weekly grocery spending of all city households

A random sample of 64 delivery times has mean 31 minutes. The population standard deviation is known to be 12 minutes. Which standard error belongs in a mean confidence interval?

12/√64 = 1.5 minutes

A random sample of 64 orders has mean completion time 78 minutes. The population standard deviation is known to be 12 minutes. For a 95% confidence interval, the supplied Excel result is NORM.S.INV(0.975) = 1.96. Which interval is correct?

.

[72.12, 83.88]

A study reports a 90% confidence interval for a population mean satisfaction score of 68 to 74. What is the best plain-language statement?

We are 90% confident the interval procedure has produced a range containing the population mean.

For a two-sided 90% confidence interval using known population σ, which Excel setup returns the positive standard-normal critical value?

=NORM.S.INV(0.95)

A sample of 41 checkout times has sample standard deviation 6.3 minutes, and population σ is unknown. Which critical-value family and df apply?

t distribution with 40 degrees of freedom

A random sample of 16 calls has mean handling time 36 minutes and sample standard deviation 8 minutes; population σ is unknown. Excel gives the two-sided 95% t critical value 2.131 with df = 15. Which interval is correct?

[31.74, 40.26]

In a sample of 250 voters, 135 favor a transit levy. What is the sample proportion and observed count check for a one-proportion interval?

54%; 135 favor and 115 do not, both at least 5

A planning team wants a 90% confidence interval for a population proportion with margin of error at most 4 percentage points. With no prior estimate, it uses planning value 0.50. The supplied Excel critical output is z* = 1.645. What minimum whole-number sample size is required?

423

A poll reports 48% support for a city proposal with a ±4 percentage-point margin of error. Which conclusion follows from the reported interval?

The interval is 44% to 52%; it includes 50%, so a population majority for support is not established by this interval.

A supplier claims a redesigned package changes the mean fill weight from 500 grams in either direction. Which alternative is appropriate?

Ha: μ ≠ 500; two-tailed test

A clinic tests whether average appointment duration differs from 30 minutes. Which describes a Type I error?

Reporting a difference from 30 minutes when the true mean is 30 minutes

A random sample of 64 transactions has mean 74; the historical population mean is 70, and population standard deviation is known to be 16. What is the one-mean z test statistic?

2.00

A known-σ test of whether a population mean exceeds its benchmark gives z = 2.11. Which Excel formula gives its right-tailed p-value?

=1-NORM.S.DIST(2.11,TRUE)

A left-tailed test of average handling time returns p = 0.012 with α = 0.01. What is the decision?

Fail to reject H0 at the 1% significance level.

A 95% confidence interval for mean delivery time is [29.1, 34.7]. What is the decision for the matching two-sided H0: μ = 32 test at α = 0.05?

A 95% confidence interval for mean delivery time is [29.1, 34.7]. What is the decision for the matching two-sided H0: μ = 32 test at α = 0.05?

A random sample of 25 service tickets has mean 67, sample standard deviation 10, and an unknown population standard deviation. Under H0 the population mean is 70. Which test statistic and degrees of freedom are correct?

t = -1.50 with df = 24

For a two-tailed one-mean t test, |t| = 2.18 and df = 34. Which expression gives the p-value?

=T.DIST.2T(2.18,34)

A two-sided t test asks whether mean store service time differs from 12 minutes. Excel reports p = 0.018. At α = 0.05, which managerial conclusion is appropriate?

There is evidence that the population mean service time differs from 12 minutes; the test alone does not quantify the size of the difference.

An AI assistant states, 'p = 0.03 proves the redesigned process increased the population mean by at least 10 units.' The planned test only asks whether the mean increased. Which audit response is strongest?

The small p-value supports an increase at α = 0.05, but the test does not by itself establish an increase of at least 10 units.

For H0: p = 0.08 and n = 80, which normal-approximation audit is correct?

np₀ = 6.4 and n(1−p₀) = 73.6; both counts are at least 5, so the rule passes.

A sample proportion is 0.37, n = 300, and H0: p = 0.40. Which expression is the one-proportion test standard error?

√[0.40(0.60)/300]

A random sample of 400 respondents includes 120 who favor a proposal. Test H0: p = 0.25. Using the null-based standard error, what is the one-proportion z statistic (to two decimals)?

2.31

A test asks whether population support is below 0.40 and produces z = −1.67. Which Excel expression is the p-value?

=NORM.S.DIST(-1.67,TRUE)

A test of whether a subscription renewal rate exceeds its benchmark returns p = 0.028. At α = 0.05, which is the defensible conclusion?

Reject H0; there is evidence the population renewal rate exceeds the benchmark.

A left-tailed z test at α = 0.05 gives z = −1.25, critical z = −1.645, and left-tail p = 0.106. What do the two rules say?

Both fail to reject H0.

A sample of 35 customers provides purchase amounts and sample standard deviation, but population σ is unknown. The claim concerns the population mean purchase amount. Which test method fits?

One-mean t test with df = 34

For a two-sided one-proportion test, a sheet reports z = 2.05 but uses =NORM.S.DIST(2.05,TRUE) as the p-value. Which correction fits?

Use =2*(1-NORM.S.DIST(2.05,TRUE)).

A poll reports 50% support for a policy with a ±2 percentage-point margin of error. What is the best response to 'the population definitely supports it'?

The interval is 48%–52%; because it includes 50%, that categorical conclusion is not justified by the interval alone.

An AI summary says a 95% poll interval of 48%–54% 'proves the policy will win the election.' What is the best repair?

The interval includes 50% and describes population support under survey assumptions; it does not prove a future election result.