79.4k views
3 votes
A study is performed in a large southern town to determine whether the average weekly grocery bill per four-person family in the town is significantly different from the national average. The national average grocery bill is $100 (standard deviation unknown). A random sample of 25 families is taken in the town, and the mean is found to be 103.23 with a standard deviation of 8.82.

For each item below, please show your work and/or explain your reasoning to receive full credit.
a). State the null and alternative hypotheses for this situation.
b). Assuming a 0.05 level of significance, compute the appropriate test statistic.
c). Find the critical t value. Can you reject the null hypothesis? Explain/justify your response using numbers and words

User NeilD
by
8.3k points

2 Answers

3 votes

Answer:

From the given problem statement

Average=$100

mean=103.23

standard deviation=8.82

Significance level=0.05

confidence level=1-0.05=99.95

The null hypothesis is given below

H0=100

H0>103.23

User Prabhat Kumar Jena
by
8.3k points
6 votes

Answer:

The average weekly grocery bill per four-person family in the town is significantly different from the national average.

Explanation:

We are given the following in the question:

Population mean, μ = $100

Sample mean,
\bar{x} = $103.23

Sample size, n = 25

Alpha, α = 0.05

Sample standard deviation, s = $8.82

First, we design the null and the alternate hypothesis


H_(0): \mu = 100\text{ dollars}\\H_A: \mu \\eq 100\text{ dollars}

We use Two-tailed t test to perform this hypothesis.

Formula:


t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }

Putting all the values, we have


t_(stat) = \displaystyle(103.23- 100)/((8.82)/(√(25)) ) = 1.831

Now,


t_(critical) \text{ at 0.05 level of significance, 24 degree of freedom } = \pm 2.063

Since,


t_(stat) < t_(critical)

We accept the null hypothesis.

We accept the null hypothesis and determine that the average weekly grocery bill per four-person family in the town is significantly same to the national average.

User Enrique Chavez
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories