Question

A market research firm used a sample of individuals to rate the
purchase potential of a particular product before and after the
individuals saw a new television commercial about the product. The
purchase potential ratings were based on a 0 to 10 scale, with
higher values indicating a higher purchase potential. The null
hypothesis stated that the mean rating "after" would be less than
or equal to the mean rating "before." Rejection of this hypothesis
would show that the commercial improved the mean purchase potential
rating. Use *α* = 0.05 and the following data to test the
hypothesis and comment on the value of the commercial.

Individual | Purchase Rating | |
---|---|---|

After | Before | |

1 | 6 | 5 |

2 | 6 | 4 |

3 | 7 | 7 |

4 | 4 | 3 |

5 | 3 | 6 |

6 | 9 | 8 |

7 | 7 | 5 |

8 | 6 | 7 |

1. State the null and alternative hypotheses. (Use
*μ*_{d} = mean rating after − mean rating
before.

2. Calculate the value of the test statistic. (Round your answer to three decimal places.)

3. Calculate the *p*-value. (Round your answer to four
decimal places.)

4. State your conclusion.

a) Do not reject *H*_{0}. There is insufficient
evidence to conclude that seeing the commercial improves the mean
potential to purchase. b) Do not Reject *H*_{0}.
There is sufficient evidence to conclude that seeing the commercial
improves the mean potential to purchase. c) Reject
*H*_{0}. There is insufficient evidence to conclude
that seeing the commercial improves the mean potential to purchase.
d)Reject *H*_{0}. There is sufficient evidence to
conclude that seeing the commercial improves the mean potential to
purchase.

Answer #1

1) Ho: ≤ 0

Ha: > 0

2) Test statistics

employee | After | Before | Diff (Aft-Bef) | Dev (diff - mean) | Sq deviation |

1 | 6 | 5 | 1 | 0.63 | 0.39 |

2 | 6 | 4 | 2 | 1.63 | 2.64 |

3 | 7 | 7 | 0 | -0.38 | 0.14 |

4 | 4 | 3 | 1 | 0.63 | 0.39 |

5 | 3 | 6 | -3 | -3.38 | 11.39 |

6 | 9 | 8 | 1 | 0.63 | 0.39 |

7 | 7 | 5 | 2 | 1.63 | 2.64 |

8 | 6 | 7 | -1 | -1.38 | 1.89 |

Total | 48 | 45 | 3 | 0.0000 | 19.8750 |

= 3/ 8 = 0.375

t stat = 0.629

(3) p value = TDIST (0.629, 7,1) = 0.2745

(4) p value is > 0.05, hence fail to reject Ho.

a) Do not reject *H*0. There is insufficient evidence to
conclude that seeing the commercial improves the mean potential to
purchase.

A market research firm used a sample of individuals to rate the
purchase potential of a particular product before and after the
individuals saw a new television commercial about the product. The
purchase potential ratings were based on a 0 to 10 scale, with
higher values indicating a higher purchase potential (meaning
people were more likely to buy the product after seeing the
commercial). The null hypothesis stated that the mean rating
“after” seeing the commercial would be less than...

A market research firm used a sample of individuals to rate the
purchase potential of a particular product before and after the
individuals saw a new television commercial about the product. The
purchase potential ratings were based on a 0 to 10 scale, with
higher values indicating a higher purchase potential. The null
hypothesis stated that the mean rating "after" would be less than
or equal to the mean rating "before." Rejection of this hypothesis
would show that the commercial...

A market research firm used a sample of individuals to rate the
purchase potential of a particular product before and after the
individuals saw a new, expensive television commercial about the
product. The purchase potential ratings were based on a 0 to 10
scale, with higher values indicating more potential to purchase the
product. You want to know if the commercial increased the mean
purchase potential rating. You will test the claim at a
significance level of αα = 0.002. To...

A market research firm used a sample of individuals to rate the
purchase potential of a particular product before
and after
the individuals saw a new television commercial about the product.
The purchase potential ratings were
based on a
0 to 10 scale, with higher values indicating a higher purchase
potential. Test whether the commercial
improved
the mean purchase potential rating. at the .10 level of
significance.
Individual
After
Before
Carl Hall
6
5
Malcom Armstead
6
4
Ron Baker...

A national study conducted by a market research firm, evaluated
the top technology companies and their reputations. The following
shows how 10 technology companies ranked in reputation and how the
companies ranked in percentage of respondents who said they would
purchase the company's stock. A positive rank correlation is
anticipated because it seems reasonable to expect that a company
with a higher reputation would have the more desirable stock to
purchase.
Company
Reputation
Stock Purchase
Company A
1
3
Company...

Periodically, customers of a financial services company are
asked to evaluate the company's financial consultants and services.
Higher ratings on the client satisfaction survey indicate better
service, with 7 the maximum service rating. Independent samples of
service ratings for two financial consultants are summarized here.
Consultant A has 10 years of experience, whereas consultant B has 1
year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has
the higher population mean service...

Consider the following hypothesis test.
H0: μ ≤ 25
Ha: μ > 25
A sample of 40 provided a sample mean of 26.2. The population
standard deviation is 6.
(a) Find the value of the test statistic. (Round your answer to
two decimal places.)
(b)Find the p-value. (Round your answer to four decimal
places.)
(c)At α = 0.01, state your conclusion.
Reject H0. There is sufficient evidence to
conclude that μ > 25.
Reject H0. There is insufficient evidence to...

Consider the following hypothesis test.
H0: μ = 15
Ha: μ ≠ 15
A sample of 50 provided a sample mean of 14.07. The population
standard deviation is 3.
(a)
Find the value of the test statistic. (Round your answer to two
decimal places.)
(b)
Find the p-value. (Round your answer to four decimal
places.)
p-value =
(c)
At
α = 0.05,
state your conclusion.
Reject H0. There is sufficient evidence to
conclude that μ ≠ 15.Reject H0. There
is...

From a random sample from normal population, we observed sample
mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80,
Ha: μ < 80. State your conclusion about H0 at significance level
0.01. Question 2 options: Test statistic: t = 1.61. P-value =
0.9356. Reject the null hypothesis. There is sufficient evidence to
conclude that the mean is less than 80. The evidence against the
null hypothesis is very strong. Test statistic: t = 1.61. P-value =
0.0644....

Consider the following hypothesis test.
H0: μ ≥ 20
Ha: μ < 20
A sample of 50 provided a sample mean of 19.3. The population
standard deviation is 2.
(a)
Find the value of the test statistic. (Round your answer to two
decimal places.)
(b)
Find the p-value. (Round your answer to four decimal
places.)
p-value =
(c)
Using
α = 0.05,
state your conclusion.
Reject H0. There is sufficient evidence to
conclude that μ < 20.Reject H0.
There is...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 18 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 31 minutes ago

asked 33 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago