Question

1 of 2

Geoff is the proud owner of a restaurant. He is interested in determining whether his Wagyu beef or Hiramasa kingfish sashimi should be marketed as the Geoff Special. Geoff has selected a random sample of 20 people to taste his Wagyu beef and give it a score out of 100. He also selected a different random sample of 20 people to taste his Hiramasa kingfish sashimi and give it a score out of 100.

The sample mean score given to the Wagyu beef dish was calculated as 67.95. The sample standard deviation of the scores for the Wagyu beef dish was calculated as 5. The sample mean score given to the Hiramasa kingfish sashimi dish was calculated as 68.65. The sample standard deviation of the scores for the Hiramasa kingfish sashimi dish was calculated as 5. The population standard deviations of the scores for each dish are unknown.

You may find this Student's t distribution table useful throughout the following questions. Note that Geoff always aims to use the easiest possible calculations, and so when using a two-sample t-test he will use the simplified formula for degrees of freedom whenever possible.

a)Geoff would like to test whether the mean scores of each of
these dishes are equal. He has constructed a hypothesis test with
H_{0}: μ_{W} = μ_{H} and H_{A}:
μ_{W} ≠ μ_{H}. Calculate the test statistic (t) for
this hypothesis test. Give your answer to 2 decimal places.

t =

b)Using the test statistic for Geoff's hypothesis test and a 95% confidence level, Geoff should accept, reject, not reject the null hypothesis.

2 of 2

A study compared the individual pre-tax yearly income earned by residents from two states. The following table lists the statistics resulting from this study:

Yearly Income | |||
---|---|---|---|

Location | Sample Size | Sample Mean ($'000s) | Sample Standard Deviation ($'000s) |

State A | 51 | 93 | 17 |

State B | 55 | 50 | 37 |

A part of the study involved calculating the upper and lower bound of the 90% confidence interval of the mean difference (State A - State B) between the income earned by individuals from the two states. For the purposes of this study, the simplified formula for the number of degrees of freedom in the appropriate t-distribution will be used. Calculate the confidence interval. Give your answers to 2 decimal places. You may find this Student's t distribution table useful.

a)Lower bound =

b)Upper bound =

Answer #1

(1a) The test statistics for testing the hypothesis is given by

where n and m are sample sizes sw and sh are sample sd's W,H are sample means and S is pooled variance

(1b)t-critical value at 95% confidence and 38 degrees of freedom(20+20-2) is 1.68 so we see that the test statistic lies between (-1.68,+1.68) so we accept the null hypothesis

(2) The (1-alpha) confidence interval for the difference of two means is given by

Considering the State A as X and State Y as B we can get the above values as

degrees of freedom and the acceptance region is thus

the interval is thus

1.) Justin is interested in buying a digital phone. He visited
15 stores at random and recorded the price of the particular phone
he wants. The sample of prices had a mean of 237.64 and a standard
deviation of 8.63.
(a) What t-score should be used for a 95% confidence interval
for the mean, μ, of the distribution?
t* = _____________
(b) Calculate a 95% confidence interval for the mean price of
this model of digital phone:
(Enter the smaller...

(1 point) Justin is interested in buying a digital phone. He
visited 9 stores at random and recorded the price of the particular
phone he wants. The sample of prices had a mean of 368.73 and a
standard deviation of 31.79.
(a) What t-score should be used for a 95% confidence interval
for the mean, μμ, of the distribution?
t* =
(b) Calculate a 95% confidence interval for the mean price of
this model of digital phone:
(Enter the smaller...

A researcher is interested in studying the effect of playing
video-games on reaction time. Specifically, he thinks that playing
a videogame will change reaction times, but he doesn’t know if it
will make subjects faster or slower. He collects the following
reaction times (in milliseconds) from a sample of 10 subjects
before and after playing a video game for one hour.
Before Playing a Video Game (T1) After Playing a Video Game (T2)
Difference Score (D) = T1-T2
360 374...

An education minister would like to know whether students at
Gedrassi high school on average perform better at English or at
Mathematics. Denoting by μ1 the mean score for all
Gedrassi students in a standardized English exam and μ2
the mean score for all Gedrassi students in a standardized
Mathematics exam, the minister would like to get a 95% confidence
interval estimate for the difference between the means:
μ1 - μ2.
A study was conducted where many students were given...

SCORES: -3, -3, -3, -3, -3, -3, -3, -3, -3,
-2, -2, -2, -2, -2, -2, -2, -2, -2,
2,
-1, -1, -1, -1, -1, -1, -1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Sample size
____36________________
Sample
mean
__-1.39______________
Sample standard
deviation
____1.29_____________
Estimated standard
error
_____.22________________
Based on the table shown in SPSS, state the following values
associated with the test statistic:
Mean
difference
___-1.39___________________
t obtained
(t)
______-6.44___________________
Degrees of freedom...

Researcher John is interested in the extent to which stress
influences human memory. He has run a study in which a random
sample of 25 participants has been told that they will be required
to give a lecture in front of a large audience. Giving a speech in
front of a large audience is considered a stressful event by many
people.
While the participants were busy preparing for their
presentation, they were asked to complete a memory task. It is...

1. A social researcher wants to test the hypothesis that people
who drink a lot while bowling have higher scores than people who do
not drink while they bowl. The researcher studies 50 drinking
bowlers and 50 non-drinking bowlers. The average score for drinking
bowlers was 142 with a standard deviation of 7.45. The average
score for non-drinking bowlers was 134 with a standard deviation of
6.81.
In words: What are your conclusions about the null
hypothesis?
2. A social...

A manufacturer is interested in the output voltage of a power
supply used is a PC. Output voltage is assumed to be normally
distributed with standard deviation 0.25 Volts, and the
manufacturer wishes to test H0: μ = 5 Volts against
Ha: μ≠ 5 Volts, using n = 8 units at 5% significance
level. If the sample mean is 5.10, then the corresponding p-value
is
0.295
0.258
0.05
1.13
) In testing the hypotheses H0: μ = 200 vs.
Ha:...

For questions 1 through 3 state the proper t-test (one
sample, paired samples, independent samples) that should be used to
evaluate the research question: (*Just state the test)
1) A developmental psychologist wants to determine if
a recently created computer training program can increase the
working memory ability of high-school students. A sample of 40
students are given the reverse digit span test at the beginning of
the school year and then again after 4 weeks of training. Are there...

In the journal Mental Retardation, an article reported the
results of a peer tutoring program to help mildly mentally retarded
children learn to read. In the experiment, the mildly retarded
children were randomly divided into two groups: the experimental
group received peer tutoring along with regular instruction, and
the control group received regular instruction with no peer
tutoring. There were n1 = n2 = 36 children in each group. The
Gates-MacGintie Reading Test was given to both groups before
instruction...

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