Question

At least 0.49 of car crashes occur within 2 miles of the motorists home.

a) Express the null and alternative hypotheses in symbolic form for this claim.

Ho: p=

Ha:


Use the following codes to enter the following symbols:
     ≥≥ enter >=
     ≤≤ enter <=
     ≠≠ enter !=

b) You decide to survey 100 adult Americans and find that 10 of car crashes occur within 2 miles of the motorists home. Find the test statistic. Round to two decimal places.

z=z=

c) What is the p-value? Round to 4 decimals.

p=p=

Based on a sample of 700 people, 55% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 4 decimals)

Based on a sample of 400 people, 87% workers got their job through networking

The test statistic is:  (to 2 decimals)

The p-value is:  (to 4 decimals)

The average student loan debt is reported to be $25,235. A student belives that the student loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean to be $27,524 and the standard devition to be $6000. Is there sufficient evidence to support the student' claim at a 5% significance level?

a) Determine the null and alternative hypotheses.

H0H0: μ=μ=

HaHa: μμSelect an answer > not = <   (Put in the correct symbol and value)

b) Determine the test statistic. Round to two decimals.

t=t=

c) Find the p-value. Round to 4 decimals.

P-value =

In 2011, a U.S. Census report determined that 71% of college students work. A researcher thinks this percentage has changed since then. A survey of 110 college students reported that 91 of them work. Is there evidence to support the reasearcher's claim at the 1% significance level?

a) Determine the null and alternative hypotheses.

H0 p=

HaH: pp

Select an answer not = < >   (Put in the correct symbol and value)

b) Determine the test statistic. Round to two decimals.

z=z=

c) Find the p-value. Round to 4 decimals.

P-value =

Answer 1

At least 0.49 of car crashes occur within 2 miles of the motorists home.

a)

As, the claim is that at least 0.49 of car crashes occur within 2 miles
Ho: p= 0.49

Ha: p $\ge$ 0.49

b)

Sample proportion = 10 / 100 = 0.1

Standard error of the proportion = $\sqrt{0.49 * (1-0.49)/100}$ = 0.04999

Test statistic, z = (Observed proportion - Hypothesized Proportion) / Standard error

= (0.1 - 0.49) / 0.04999 = -7.8

c)

P-value = P(z > -7.8) = 1

As, p-value is greater than significance level 0f 0.05, we fail to reject H0 and conclude that there is no significant evidence that p $\ge$ 0.49 (at least 0.49 of car crashes occur within 2 miles of the motorists home)