Question

1.)You intend to estimate a population mean μμ from the following sample.

37.2
50.5
8.5
43.3
24.9
28
31.1
37.5
46.8
19.2

You believe the population is normally distributed. Find the 95% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).

95% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

2.)

In a survey, 61 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $34 and standard deviation of $9. Construct a confidence interval in the form estimate ± margin of errorestimate ± margin of error at a 98% confidence level.

±±  Give your answers to one decimal place.

3.)Out of 100 people sampled, 41 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to three places.

< p <

4.)You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.      

Ho:μ=66.4Ho:μ=66.4
      Ha:μ≠66.4Ha:μ≠66.4

You believe the population is normally distributed and you know the standard deviation is σ=18.1σ=18.1. You obtain a sample mean of ¯x=61.8x¯=61.8 for a sample of size n=75 n=75.

What is the test statistic for this sample?

(Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =  The p-value is...

5.)

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.      

Ho:μ=86.7Ho:μ=86.7
Ha:μ<86.7Ha:μ<86.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=10n=10 with mean ¯x=62.8x¯=62.8 and a standard deviation of s=19.4s=19.4.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 3 decimal places
   
2. What is the p-value for this sample?
   
   p-value =  Use Technology Round to 4 decimal places.

Answer 1

(1) To construct 95% confidence interval for the population mean with the given sample data, we first need to calculate the sample mean and sample standard deviation , and the formula for confidence interval is given by-

Sample mean:

Sample standard deviation:

Critical value:

So the 95% confidence interval for the population mean is calculated as .

_________________________

(2) The formula for confidence interval is given by

Given:

Critical value: For 98% confidence

98% confidence interval for the population mean :

______________________________--

(3) The formula for confidence interval for the population proportion is given by-

Sample proportion:

sample size, n=100

Critical value: For 99% confidence

The 99% confidence interval for the true population proportion of people who have kids is calculated as , i.e.,

_________________________

(4) The null and alternative are:

Null hypothesis,

Alternative hypothesis,

Given:

Test-statistic: Since the population, standard deviation is given then the test-statistic is calculated as -

P-value: The test statistic is calculated as , and we are testing a two-tailed hypothesis then the p-value is calculated as -

Decision: Significance level, and

__________________________

(5) The null and alternative hypothesis are:

Null hypothesis,

Alternative hypothesis,

Given:

Test-statistic: Since the population standard deviation is unknown, then the test statistic is given by the formula-

P-value: Since we are testing a left-tailed hypothesis and the test statistic is calculated as -

Decision: Significance level is given as and the p-value is