Question

A researcher believes that community B has a lower income than
community A. Forty people are surveyed in each of the two
communities regarding their income. In place A, the mean among the
40 individuals is 62 (given in thousands; you can ignore the
‘thousands’ and just use ‘61’), and the variance is 95; in place B,
the mean among the 40 surveyed is 59, and the variance is
100. Test the null hypothesis that the two communities
have equal incomes. Use alpha = 0.05. State the null and
alternative hypotheses, find the test statistic, compare it with
the critical value, make a decision, and find the
*p*-value.

Thank you!

Answer #1

Null and alternative hypothesis is

Ho: mu1 = mu2

Ha: mu1>mu2

Where mu1 and mu2 are average income of community A and community B respectively

Test statistic

Z = (x1bar-x2bar) / sqrt(sigma1^2/n1 + sigma2^2/n2)

Where x1bar and x2bar are sample average income of community A and B. n1 and n1 are respective sample size

Z = (62-59) / sqrt(95^2/40 + 100^2/40)

= 3/21.81

= 0.137

Critical value at 5% of one tailed z test is 1.645. Since test statistic is less than 1.645, we fail to reject Ho at 5%. Hence researcher claim is not correct. P value corresponding to one tailed z test with test statistic z = 0.137 is 0.445

A researcher believes that community B has a lower income than
community A. Forty people are surveyed in each of the two
communities regarding their income. In place A, the mean among the
40 individuals is 62 (given in thousands; you can ignore the
‘thousands’ and just use ‘61’), and the variance is 95; in place B,
the mean among the 40 surveyed is 59, and the variance is
100. Test the null hypothesis that the two communities
have equal...

4. A researcher believes that the proportion of a community’s
population in favor of a new park is greater than the countywide
proportion of 0.65. A survey of 67 people in the community reveals
that the estimated proportion of the community in favor of it is
equal to 0.76. Use alpha = 0.05. State the null and alternative
hypotheses, find the test statistic, compare it with the critical
value, make a decision, and find the p-value.

A researcher believes that the proportion of a community’s
population in favor of a new park is greater than the countywide
proportion of 0.65. A survey of 67 people in the community reveals
that the estimated proportion of the community in favor of it is
equal to 0.76. Use alpha = 0.05. State the null and alternative
hypotheses, find the test statistic, compare it with the critical
value, make a decision, and find the p-value.

4. A researcher believes that the proportion of a community’s
population in favor of a new park is greater than the countywide
proportion of 0.65. A survey of 67 people in the community reveals
that the estimated proportion of the community in favor of it is
equal to 0.76. Use alpha = 0.05. State the null and alternative
hypotheses, find the test statistic, compare it with the critical
value, make a decision, and find the p-value.
PLEASE HELP!

A medical researcher wants to compare the pulse rates of smokers
and non-smokers. He believes that the pulse rate for smokers and
non-smokers is different and wants to test this claim at the 0.1
level of significance. A sample of 76 smokers has a mean pulse rate
of 79, and a sample of 62 non-smokers has a mean pulse rate of 76.
The population standard deviation of the pulse rates is known to be
7 for smokers and 8 for...

A sociologist believes that for people under the age of 30,
women sleep longer per night on the weekend than men. 16 people
were surveyed. Test at alpha =5%. The following summary statistics
were determined from the sample.
Men:
Mean hrs = 10.45
SD hrs = 0.95
n=9
Women:
Mean hrs = 11.18
SD hrs = 1.81
n=7
a) State the Null and Alternate Hypothesis in symbols and in
words.
b) Calculate the expected results for the hypothesis test
sampling...

Here is a link to a data set concerning treatment groups A and
B. Before performing a t-test to determine if the two groups are
different, researchers must first ascertain if the variance in the
two groups is the same using an F test. Indicate whether the
hypothesis below is the null or alternate hypothesis for the F
test. null The variance in group A is equal to the variance in
group B Calculate the F statistic for this data...

A medical researcher wants to compare the pulse rates of smokers
and non-smokers. He believes that the pulse rate for smokers and
non-smokers is different and wants to test this claim at
the 0.05 level of significance. A sample
of 72 smokers has a mean pulse rate of 75, and a
sample of 81 non-smokers has a mean pulse rate of 72.
The population standard deviation of the pulse rates is
known to be 6 for smokers and 9 for...

A medical researcher wants to compare the pulse rates of smokers
and non-smokers. He believes that the pulse rate for smokers and
non-smokers is different and wants to test this claim at the 0.05
level of significance. A sample of 72 smokers has a mean pulse rate
of 75, and a sample of 81 non-smokers has a mean pulse rate of 72.
The population standard deviation of the pulse rates is known to be
6 for smokers and 9 for...

You are a social worker who works in a community center in a
lower-income neighborhood. You have been asked to work with a
university researcher who wants to determine whether residents of
this neighborhood support capital punishment. To do this, you
recruit 16 residents to participate in your study and you
administer the Support for Capital Punishment Scale (30 dichotomous
items, range 0-30) to a sample of 16 individuals who are equally
divided among four age categories. The scores are...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 26 minutes ago

asked 34 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago